dielectric and piezoelectric properties of reduced-graphite...

Dielectric and Piezoelectric Properties of Reduced-Graphite-

Oxide/Poly(vinylidene fluoride) Nanocomposite and its Related

Devices

Ye Zhang

Submitted in partial fulfilment of the requirements of

the Degree of Doctor of Philosophy

School of Metallurgy and Materials,

University of Birmingham

Birmingham, United Kingdom

September 2018

University of Birmingham Research Archive

e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.

Ph.D Thesis – Ye Zhang

i

Declaration

I, Ye Zhang, confirm that the research included within this thesis is my own work or

that where it has been carried out in collaboration with, or supported by others, that this

is duly acknowledged below and my contribution indicated. Previously published

material is also acknowledged below.

I attest that I have exercised reasonable care to ensure that the work is original, and does

not to the best of my knowledge break any UK law, infringe any third party’s copyright

or other Intellectual Property Right, or contain any confidential material.

I accept that the College has the right to use plagiarism detection software to check the

electronic version of the thesis.

I confirm that this thesis has not been previously submitted for the award of a degree by

this or any other university.

The copyright of this thesis rests with the author and no quotation from it or information

derived from it may be published without the prior written consent of the author.

Ye Zhang

09/2018


ii

Acknowledgement

Firstly, I would like to thank my supervisor Professor Tim Button for guiding me

through my PhD project in the past four years. Tim has always been nice and patient to

discuss with me on my projects and gave me caring support when I got difficulties.

Secondly, I would like to thank my second supervisors Dr. Yun Jiang and Dr. Daniel

Rodriguez Sanmartin, for their kindly help and support. And I also want to express my

appreciation to Mr. Carl Meggs, who assisted me a lot in the lab. Furthermore, I would

like to thank my colleagues and friends for their help and support in my research. I

would like to thank the Chinese Scholarship Council for providing me with financial

support for my PhD program.

My greatest thanks go to my grandparents Ms. Shuhe Lin, Mr Chunhai Hao, my parents

Ms. Yueguang Hao and Mr. Beicheng Zhang for their all-time support in my life and

career. Special thanks go to my wife Ms. Yaqiong Wang, who is a studying PhD in

Queen Mary, University of London, not only for her understanding, love and care, but

also for being the most important person in my life.


iii

Abstract

There is an increasing demand of smart devices with light-weight, flexible, and scalable

nature. Functional polymers and the related composites are suitable candidates that can

fulfil the requirements in flexible device applications. Poly(vinylidene fluoride) (PVDF)

is one kind of the functional polymers possessing a large dielectric strength as well as a

permanent molecular electrical dipole (for all-trans and semi-trans conformation).

Hence, it has the potential to be applied to capacitive energy storage devices as well as

piezoelectric sensors and actuators. One route to improve the dielectric and piezoelectric

of the PVDF polymer is to hybridize the pure polymer with an inorganic inclusion

phase, usually submicron-sized ferroelectric ceramic particles or nano-sized low-

dimensional carbons. As these composites always suffer poor dispersion and exhibit

high leakage, majority of attentions have been focused on fabrication-structure relation

to solve the processing issues. In this project, we focused more on the structure-property

relation of the PVDF related composites. The aim of this project is to give deeper

understandings in the potential and limitations for PVDF related composites and

provide a guidance on optimizing the dielectric and piezoelectric properties these

composites for flexible devices.

The reduced-graphite-oxide (rGO) was chosen as the inclusion particles, and the

rGO/PVDF nanocomposites were fabricated via an in-situ thermal reduction method. To

start, we studied the role of rGO on the dielectric properties of the nanocomposites.

With a conductor-insulator heterostructure model, we found an ‘expanding’ effect of

rGO particles that improves the system dielectric response. We also found a pseudo-

leakage in nanocomposites due to charge carrier recombination. These findings


iv

established a quantitative method to evaluate the energy storage performance for

capacitors with composite dielectrics, which fits well with the experimental data.

We also studied the molecular and crystal structure of the PVDF polymer with respect

to the rGO addition. It was found that the addition of rGO can induce the nucleating of a

thermodynamically instable β phase, which makes the nanocomposites ferroelectric.

This β phase formation was found to occur in the melting-recrystallization procedure,

which is accompanied by the thermal reduction of rGO. Based on the experimental data,

a β phase formation mechanism was proposed, which suggests the nanocomposites is

piezoelectric with PVDF molecular dipole mirrored by the rGO plane forming local

bimorph structure. According to this, two types of piezoelectric devices with the

rGO/PVDF nanocomposites were fabricated and tested, and the results are in good

agreement with the models proposed in this research.


v

Table of Contents

Declaration ......................................................................................................................... i

Acknowledgement............................................................................................................. ii

Abstract ............................................................................................................................ iii

Table of Contents .............................................................................................................. v

List of Figures .................................................................................................................. ix

Nomenclature and Acronyms .......................................................................................... xv

Chapter 1 Introduction ................................................................................................. 1

Chapter 2 Fundamentals of Ferroelectricity ................................................................ 4

2.1 Non-centrosymmetric Crystals ........................................................................... 4

2.2 Piezoelectric Materials ....................................................................................... 5

2.3 Pyroelectric Materials ......................................................................................... 8

2.4 Ferroelectric Materials...................................................................................... 10

Chapter 3 Poly(vinylidene fluoride) Ferroelectric Polymers ..................................... 16

3.1 Conformational and Crystal Structure .............................................................. 16

3.2 Ferroelectricity in PVDF Polymers .................................................................. 22

3.3 PVDF Composites with Inorganic Inclusions .................................................. 23

3.4 β-Phase Formation in PVDF Composites ........................................................ 31

Chapter 4 Aim and Objectives ................................................................................... 35

Chapter 5 Experimental and Measurement Methods ................................................. 36


vi

5.1 Solution-casting of Pure PVDF film ................................................................ 36

5.2 Solution-casting of the GO/PVDF Nanocomposites ........................................ 36

5.3 In-situ Thermal Reduction of the GO Particles ................................................ 38

5.4 In-situ Thermal Reduction of the GO/PVDF Nanocomposites ........................ 38

5.5 Lapping and Electrode-Sputtering the rGO/PVDF Nanocomposites ............... 39

5.6 Measurement Techniques ................................................................................. 40

Chapter 6 Modelling the Dielectric Behaviour of a Composite ................................ 45

6.1 Introduction ...................................................................................................... 45

6.2 Schottky Junction Theory and Device Capacitance ......................................... 45

6.3 Modelling of the rGO/PVDF heterointerface ................................................... 49

6.4 Morphology and Structure of rGO and rGO/PVDF Nanocomposites ............. 55

6.5 I-V Characteristics of the rGO/PVDF Nanocomposites .................................. 59

6.6 Equivalent Circuit of the rGO/PVDF Nanocomposites ................................... 62

6.7 Summary .......................................................................................................... 65

Chapter 7 Dielectric Behaviour of the rGO/PVDF Nanocomposites ........................ 66

7.1 Introduction ...................................................................................................... 66

7.2 Dielectric Responses of the rGO/PVDF Nanocomposites ............................... 66

7.3 Energy Storage Performances of the rGO/PVDF Nanocomposites ................. 70

7.4 Modifying the rGO/PVDF Heterojunction for Achieving Large Discharge

Energy Density ............................................................................................................ 75

7.5 Relation Between Dielectric Permittivity and Discharge Energy Density ....... 78


vii

7.6 Summary .......................................................................................................... 80

Chapter 8 β-Phase Formation in the rGO/PVDF Nanocomposites ........................... 82

8.1 Introduction ...................................................................................................... 82

8.2 Molecular Conformation in the rGO/PVDF Nanocomposites ......................... 83

8.3 Crystalline Structure of the rGO/PVDF Nanocomposites ............................... 88

8.4 Morphology and Local Piezoelectric Response of the rGO/PVDF

Nanocomposites .......................................................................................................... 93

8.5 Formation Mechanism of β Phase in the rGO/PVDF Nanocomposites ........... 94

8.6 Summary .......................................................................................................... 98

Chapter 9 rGO/PVDF Nanocomposite Related Devices ......................................... 100

9.1 Introduction .................................................................................................... 100

9.2 Actuator Assembly and Measurement Configuration .................................... 100

9.3 Vibrational Characteristics of the Nanocomposite ......................................... 104

9.4 Energy Harvester Assembly and Measurement Configuration ...................... 106

9.5 Output Characteristics of the Energy Harvesters ........................................... 112

9.6 Summary ........................................................................................................ 116

Chapter 10 Conclusion and future work .................................................................... 118

10.1 Conclusion .................................................................................................. 118

10.2 Future work ................................................................................................. 121

Reference....................................................................................................................... 123

Publications ................................................................................................................... 131


viii

Appendix ....................................................................................................................... 132


ix

List of Figures

Figure 2.1 The relationship of ferroelectric, pyroelectric and piezoelectric materials ..... 5

Figure 2.2 Crystal structure of ZnO showing an unswitchable dipole moment due to

alternating Zn2+ (black sphere) and O2- (grey sphere) planes[1] ....................................... 7

Figure 2.3 Illustration of the pyroelectric effect. An increase in temperature T reduces

the spontaneous polarization Ps causing change in surface charge. This will induce a

current flow to composite the change in surface charge.[12] ......................................... 10

Figure 2.4 Schematic view of the structure of the different phases of BaTiO3. The Ba2+

ions (large sphere) are located at the corners, the Ti4+ ions (medium sphere) at the centre,

and the O2- (small sphere) ions at the face centres. The arrows show the polar direction

along the cubic [001] direction for the tetragonal phase, the [011] direction for the

orthorhombic phase, and the [111] direction for the rhombohedral phase.[16] .............. 12

Figure 2.5 P-E hysteresis loop parameters for ferroelectric material[18] ....................... 13

Figure 2.6 Electric displacement-electric field (D-E) loop measurement of NKN850

ceramics at 1Hz and 25°C. (a) Electric field versus time and current versus time (b)

current-electric field (I-E) hysteresis loop, (c) electric displacement-electric field (D-E)

loop.[19] .......................................................................................................................... 15

Figure 3.1 Molecular packing and crystal structure. (a), (b), Schematic packing of two

polymer chains with the TGT� configuration in the unit cell of the α-phase and the δ-

phase. The symbols present the in- and out-of-plane components of the dipole moment.

In the α-phase all contributions cancel out. In the δ-phase the in-plane components

cancel out but the out-of-plane ones yield a net microscopic dipole moment. (c), (d),

The crystal structures and molecular packing of α-PVDF and δ-PVDF viewed along the

c axis. The polymer chain is projected onto the ab-plane. (e), (f), Crystal structure of α-


x

PVDF and δ-PVDF viewed along the a axis. The drawn inner lines represent the unit

cells. Grey circles represent carbon atoms, red circles fluorine atoms and blue circles

hydrogen atoms[25] ........................................................................................................ 18

Figure 3.2 Comparison of the unit cell of the (a) α phase and (b) β phases. The yellow

sphere is the carbon, the red sphere is fluorine, and the white sphere is hydrogen, (c) and

(d) are the molecular structure of α phase and β phase.[28] ........................................... 19

Figure 3.3 Molecular conformation and chain packing for γ-PVDF[30] ........................ 20

Figure 3.4 Relation between PVDF phase and processing conditions, DMA is short for

dimethylacetamide while HMPTA is short for hexamethylphosphoramide [33] ........... 22

Figure 3.5 Schematic illustration for the preparation of fluoro-polymer@BaTiO3

nanoparticles and P(VDF-HFP) nanocomposite films[48] ............................................. 25

Figure 3.6 (a) Image of the graphene oxide and nanocomposite: (a) the in situ reduced

process for the single layer reduced-graphene oxide nanocomposite, (b) digital image of

graphene oxide and in situ reduced-graphene oxide nanocomposite[57] ....................... 26

Figure 3.7 A metal electrode-dielectric interface showing (a), positive metal cores; (b),

the outer electron cloud of the metal; (c), the structured inner Helmholtz layer of

molecules and ions; (d), the outer Helmholtz layer and (e), the Gouy-Chapman diffuse

space charge layer. The arrow indicate the orientation of polar molecules, and the

molecules at the inner Helmholtz layer is highly ordered compared to those at the

diffusion layer. [63] ......................................................................................................... 30

Figure 3.8 Finite element model of two phase composites with varying volume fraction

of the conducting phase. Upper images show example random distributions of the

conductor (gray) in a dielectric matrix (cyan), and lower images are corresponding


xi

contour plots after application of a normalized external electric field (Eapplied=1). For a

filler-free matrix, Elocal=1 at all locations.[66] ................................................................ 31

Figure 3.9 Simulation model describing (a), (b) TGT� and (c), (d) TTTT chains

absorbed on the armchair CNT tube, (e), (f) TGT� and (g), (h) TTTT chains absorbed

on the zig-zag CNT tube[71]........................................................................................... 33

Figure 3.10 Schematic representation of the interaction between CoFe2O4 nanoparticles

and PVDF chains in the nanocomposite: the partially positive C–H bonds of the

polymer are attracted by the negatively charged ferrite surface due to the static electric

force. This leads to the all-trans conformation of the polymer phase[67] ...................... 34

Figure 5.1 Photograph comparing the dispersity of (a) GO and (b) xGnP in DMF

solvents after sonication for 12h and 4 days of sedimentation ....................................... 38

Figure 5.2 Photograph comparing the (A) PVDF film annealed at 200°C for 1h, (B)

GO/PVDF film annealed at 100°C for 1h and (C) rGO/PVDF film annealed at 200°C

for 1h ............................................................................................................................... 39

Figure 5.3 The route of IR beam in ATR-IR spectroscopy[78] ...................................... 41

Figure 5.4 Illustration of the AFM/PFM method, with the sample deforms to respond to

the applied voltage [79,80] .............................................................................................. 43

Figure 6.1 Electrical structure of a metal and a semiconductor (a) before contact and (b)

after contact ..................................................................................................................... 47

Figure 6.2 (a) a diode model resembles a conductor/insulator type composite and (b)

illustration for the effective expansion of composite system electrode by the addition of

inclusion particles............................................................................................................ 51

Figure 6.3 Illustration of carrier recombination induced pseudo-leakage. ..................... 54


xii

Figure 6.4 (a) X-ray diffractions for raw graphite and graphite-oxide prepared via

Harmmer’s method, and Morphology of (b) GO particles and (c) rGO particles reduced

at 200°C for 1h in N2 atmosphere ................................................................................... 56

Figure 6.5 ATR-IR spectra for GO and rGO particles reduced at 200°C for 1h. ........... 58

Figure 6.6 (a) SEM image of (a) as-casted GO/PVDF nanocomposites, (b) rGO/PVDF

nanocomposites reduced at 200°C for 1h, and (c) pure PVDF annealed at 200°C for 1h.

......................................................................................................................................... 59

Figure 6.7 I-V curve of 50µm rGO/PVDF nanocomposites coated with φ1mm

chrome/gold electrode with different rGO content, in comparison with a pure PVDF, the

insert figure shows the fitted results of I0 and Rs ............................................................ 62

Figure 6.8 Nyquist plot of pure PVDF and rGO/PVDF nanocomposites, and their

corresponding equivalent circuits ................................................................................... 64

Figure 7.1 Frequency domain of (a) relative dielectric permittivity and (b) tanδ of 0.015-

rGO-PVDF nanocomposites reduced at the temperature range from 100°C to 200°C for

1h ..................................................................................................................................... 68

Figure 7.2 Frequency domain of (a) relative dielectric permittivity and (b) tanδ of rGO-

PVDF nanocomposites reduced at 200°C for 1h ............................................................ 70

Figure 7.3 (a) discharging energy density Jd, (b) dielectric strength, and (c) efficiency η

vs. field strength E for nanocomposites reduced at 200°C with varies of rGO content . 73

Figure 7.4 (a) D-E loops of 1.5-rGO@200 showing field-gated leakage and carrier

recombination induced overcharging effect, and (b) band distortion between rGO

particles illustrating the kinetics of carrier recombination .............................................. 75

Figure 7.5 D-E hysteresis loops measured at 50MV/m at 10Hz for 1.5-rGO

nanocomposites reduced in the temperature range between 100°C and 160°C .............. 76


xiii

Figure 7.6 Effect of reduction temperature on the (a) dielectric strength, (b) discharging

energy density Jd and (c) efficiency η of 0.015-rGO ...................................................... 78

Figure 7.7 Plots of discrete efficiency-charge displacement pairs measured from both

pure PVDF and nanocomposite devices with varies reduction temperature and rGO

content, the solid curve is the fitting result of the PVDF device, which fits well with the

nanocomposites data, insert figure compares the experimental and calculated discharge

energy density for two nanocomposite devices. ............................................................. 80

Figure 8.1 ATR-IR spectra of pure PVDF and rGO/PVDF nanocomposites ................. 84

Figure 8.2 ATR-IR spectra comparing pure PVDF and rGO/PVDF nanocomposites at

annealing temperatures ranging from 100°C to 200°C, with IR wavenumber between (a)

775cm-1 to 950cm-1, and (b) 975cm-1 to 1350cm-1 .......................................................... 86

Figure 8.3 Dielectric permittivity vs. temperature plots for an as-casted 1.5-rGO and an

as-casted pure PVDF ....................................................................................................... 87

Figure 8.4 XRD spectra for PVDF and nanocomposites annealed at 200°C, the peaks

marked by * is assigned to the substrate ......................................................................... 89

Figure 8.5 Fitting curves with Lorenz peak function for (a) pure PVDF and (b) to (e) the

nanocomposites reduced at 200°C .................................................................................. 90

Figure 8.6 (a) content of β(110)/(200) and α(100) in the crystalline forms, (b) content of

α(100) in the α phase and its FWHM changes with respect to the rGO volume fraction,

and (c) illustration of the β(110)/α(100) stack structure in the nanocomposite sample. . 92

Figure 8.7 AFM images for (a) 1.0-rGO@200 and (b) pure PVDF indicate the

nanocomposite possess rougher surface of agglomerated spherulites, PFM images for (c)

1.0-rGO@200 and (d) pure PVDF show cross-talk signal from morphology fluctuation,


xiv

therefore we applied a -30V to 30V DC sweep to individual points to test the local

electromechanical response, which are plotted in (e) to (g)............................................ 94

Figure 8.8 (a) Comparison of the homogeneous nucleation (N(homo)) in pure PVDF

and heterogeneous nucleation (N(hetero)) in the nanocomposite, (b) β phase formation

due to TTTT molecule absorption and packaging at the rGO surface forming electrical

double layer structure in the PVDF melt, assuming rGO is positively charged, the build-

in field of PVDF dipole (indicated as an arrow) will counter-balance the static field of

the rGO surface charge and (c) illustration of symmetrical PVDF dipole (white arrow)

on the rGO (black line) surface forming a self-bimorph in the nanocomposite ............. 98

Figure 9.1 (a) Vibration regime of a bi-clamped actuator device with respect to the

electric field and (b) the vibration measurement configuration .................................... 103

Figure 9.2 Strain responses of BCAs assembled with (a) commercial PVDF film and (b)

0.015-rGO@200 nanocomposite operating at 100V/mm 20kHz ................................. 105

Figure 9.3 (a) Structure of a cantilever type energy harvester with rGO/PVDF

nanocomposite and (b) the voltage output measurement configuration ....................... 108

Figure 9.4 Voltage output of a single-end-clamped energy harvester driven by finger

tapping under (a) forward connection and (b) reverse connection ............................... 110

Figure 9.5 Relation between cantilever shape and the voltage output for the energy

harvester with 1.5-rGO@200 ........................................................................................ 111

Figure 9.6 Open circuit voltage output vs. load mass for 1.5-rGO-TCEH ................... 112

Figure 9.7 Illustration of the internal screening effect in a capacitive device. ............. 116


xv

Nomenclature and Acronyms

tanδ dissipation factor

Φb Schottky barrier

ψ Fermi level equalization energy

ε0 vacuum dielectric permittivity

ε dielectric permittivity

εr relative dielectric permittivity

η energy efficiency

θ angle

κ Debye-Huckel parameter

λ wavelength

ν magnification coefficient

ζ damping ratio

σ charge density

τ relaxation time

φ surface potential

ω angular frequency

A junction area

A* Richardson constant

C capacitance

D electrical displacement

E electric field

E* local electric field

F texture quality


xvi

G Gibbs free energy

I current

J energy density

Jd discharge energy density

N density of states

Q constant phase element

R resistance

S strain

T temperature

Tm melting temperature

U volume

V surface bias

Voc open circuit voltage

X phase content

Z PFM amplitude

a, b, c lattice parameter

d33 longitudinal piezoelectric constant

d31 transverse piezoelectric constant

e charge of an electron

f volume fraction

k Boltzmann constant

n number density of charge carriers

p polarization density

t thickness


xvii

w width of the depletion/accumulation layer

GO graphite oxide

rGO reduced graphite oxide

CNT carbon nanotube

PVDF poly(vinylidene fluoride)

DMF N, N-dimethylformamide

MFC microfibre composite

1.0-rGO@200 nanocomposite with 1.0 vol.% rGO reduced at 200°C

EDL electrical double layer

TCEH triangular cantilever energy harvester

BCA bi-clamped cantilever actuator

SEM scanning electron microscope

XRD X-ray diffraction

FTIR Fourier transformation infrared

ATR-IR attenuated total reflection-infrared

AFM atomic force microscope

PFM piezoforce microscope

TTTT all trans PVDF molecular chain

TTT�̅ semi-trans PVDF molecular chain

TGT�̅ trans-gauche PVDF molecular chain


1

Chapter 1 Introduction

Recent developments in aerospace and civil industries call for high performance

ferroelectric materials that are durable, lightweight, and flexible to fulfil the application

demands. The most widely reported solution is to incorporate the brittle ferroelectric

ceramic into a soft polymer environment in hoping to combine the advantages of both

materials. For instance, NASA used a macro fibre composite (MFC) as a sensor for

ground vibration testing of their inflatable satellites. The MFCs are composed of PZT

fibre and epoxy matrix and are highly flexible and lightweight, which can be integrated

unobtrusively into the skin of a torus or space device forming an attractive testing

arrangement. In addition, the functional material group (FMG) in University of

Birmingham developed a needle-shape ultrasound transducer based on fine-scaled 1-3

PZT/epoxy composites for image guided neurosurgery. The enhanced durability and

scalability of 1-3 composites make them possible to fit a Ф1.8mm transducer head

while the composite structure also results in an increased electrical mechanical coupling

and reduced the overall acoustic impedance that lead to a promising signal to noise ratio.

However, the fabrication of ceramic/polymer composites, particularly those with fine-

scaled structure, is still quite challenging, which can make them expensive solutions for

practical uses. Besides, the relatively high solid loading of ceramic fillers also reduces

flexibility of the composites.

Another solution that naturally existed is the polar polymers, and good examples can be

poly(vinylidene fluoride) (PVDF) and its bi- and tri-polymer derivatives. The PVDF

polymer possess at least 4 crystal structures, and three of these possess spontaneous

polarizations due to the inter- and intramolecular dipole moment. This is to say, PVDF


2

can simultaneously possess ferroelectric properties and the polymeric advantages such

as lightweight and flexibility. However, the relatively low ferroelectric properties

compared to the ceramic counterparts hinders their application potential. For instance,

the relative dielectric permittivity of the pure PVDF, which originates from the dipole

polarization in ferroelectrics, is merely 8~19 (at 1kHz), compared to that of over 1000

in pure ferroelectric ceramics. The piezoelectric constant d33 17~50 pC/N, which is also

significantly lower than that of the pure ferroelectric-ceramics. The most up-to-date

approaches in enhancing the ferroelectric performance of the pure PVDF polymers is to

incorporate conductive nano particles into the PVDF matrix, with carbon nanotube

(CNT) and graphene (or a-few-layer graphite) being the most reported. Unlike the

ceramic/polymer composites, the addition of CNT or graphene not only enhances the

dielectric and piezoelectric performances of the pure polymer, but also leads to a higher

mechanical strength. The conductive-nano-particle/polymer composites have been a

popular topic for a decade, but there are still issues pending to be addressed. One major

issue is the high dielectric loss associating to the addition of conductive particles. As

these carbon nano particles typically possess a low percolation threshold, loss is very

significant even at small solid loadings, which hinders their ferroelectric properties

particularly at strong electric fields.

This thesis investigates the theoretical aspects of the reduced-graphite-oxide

(rGO)/PVDF nanocomposites, with attention being focused on the impact of the

heterointerfaces on the ferroelectric properties. Chapter 2 is a review of the

fundamentals of ferroelectrics while Chapter 3 introduces the most up-to-date results

reported in the theory and application of PVDF polymers and their composites. The aim

and scope of the work are listed in detail in Chapter 4. Chapter 5 focuses on the


3

experimental procedure for fabricating and characterizing the rGO/PVDF

nanocomposites. A general model concerning the dielectric behaviour of a

conductor/insulator composite is established in Chapter 6, which serves as the

fundamentals for this project. Chapter 7 studies the energy storage capability of the

rGO/PVDF composites and discussed with the model in Chapter 6. Chapter 8 focuses

on the origin of polar conformation transition for PVDF molecule with respect to the

rGO addition in the melting-recrystallization procedure. A unique symmetrical

molecular dipole configuration to the rGO plane is also indicated. Chapter 9 assess the

potential of rGO/PVDF nanocomposites in piezoelectric devices. Two devices were

fabricated and tested, with one being a cantilever unimorph and the other being a

flexible energy harvester. The findings of this project as well as the future work are

summarized in chapter 10.


4

Chapter 2 Fundamentals of Ferroelectricity

2.1 Non-centrosymmetric Crystals

The symmetry of crystal can be described by 32 point groups. Any point in the unit cell

can be defined by coordinates x, y, and z, with respect to the origin of symmetry. If the

movement of this point from position (x,y,z) to position (-x, -y, -z) does not induce any

difference, then the crystal can be called as a centrosymmetric crystal. Otherwise, the

crystal is a non-centrosymmetric crystal. In terms of the centrosymmetric crystals, the

centre of positive and negative charges will coincide, resulting in a zero net charge in

the unit cell. While in terms of the non-centrosymmetric crystals, the separation of the

centre of positive and negative charges produces a dipole moment with a built-in

electric field opposite to the dipole orientation. This built-in potential will result in a

charged state on the boundary of the unit cell. Due to this dipole moment, non-

centrosymmetric crystals can respond to external stimuli such as electric field or heat,

thus materials assembled with non-centrosymmetric crystals can possess unique

functional properties for active device applications.

Out of 32 point groups, 21 point groups possess the non-centrosymmetric nature and

exhibit piezoelectricity, in which the crystal can generate a strain response to the applied

electric field and vice versa. 10 out of these 21 point groups possess spontaneous

polarization (permanent dipole moment) in the absence of an electric field, which are

classed as ferroelectric. If the spontaneous polarization changes with respect to

temperature, then the crystal is pyroelectric. While if the spontaneous polarization can

be permanently reoriented by the electric field, the crystal is then ferroelectric. Figure

2.1 shows the relationship of piezoelectric, pyroelectric, and ferroelectric materials. As


5

seen, all ferroelectric materials are pyroelectric and piezoelectric. Good examples can

be perovskite ceramics such as Barium-Titanite (BaTiO3) and Lead-Zirconite-Titanite

(PbTixZr(1-x)O3) which possess polarization switching characteristics with respect to the

electric field. Polar crystals without the switching behaviour is pyroelectric but not

ferroelectric. Examples of this kind of material can be found in ZnO in which the dipole

moment is aligned with the crystal orientations and is non-switchable.[1] Non-

centrosymmetric crystals with non-polar structure can generate an instantaneous dipole

moment with respect to the stress or electric field, which is solely piezoelectric.

Examples can be found in SiO2 and GaAs crystals, in which there is no net dipole

moment in static conditions.[2,3]

Figure 2.1 The relationship of ferroelectric, pyroelectric and piezoelectric materials

2.2 Piezoelectric Materials

The pre-fix piezo- is derived from the Greek word, which means to squeeze or press.

Therefore, piezoelectricity defines the electric field induced strain (reverse piezoelectric

effect) or strain induced charge displacement (direct piezoelectric effect) phenomena in

a material. The history of piezoelectricity can be dated back to 1880, when Jacques and


6

Pierre Curie demonstrated the direct piezoelectric effect in the research of quartz and

Rochelle salt (KNaC4H4O6·4H2O).[4] Later, the reverse piezoelectric effect was also

mathematically demonstrated by Gabriel Lippmann in 1881.[5] In the next few decades,

piezoelectricity was only something of laboratory curiosity until the invention of

Barium Titanite (BaTiO3), which is a milestone in piezoelectricity.[6] Till now,

piezoelectric materials have been used in a wide variety of applications such as sensors

(direct piezoelectric effect) and actuators (converse piezoelectric effect), which are

crucial components in modern industry.

The piezoelectric effect can be attributed to the dipole moment within the unit cell of

the material, which originates from the non-centrosymmetric nature of the crystal

structure. Figure 2.2 shows the crystal structure of Zinc Oxide (ZnO), which can be

used to interpret the relationship between the piezoelectric effect and crystal structure.

ZnO possess a hexagonal lattice structure and belongs to the P63mc space group without

a centre of symmetry.[7] This is because the alternating Zn2+ and O2- planes in the c-

axis, which induce the termination of [0001] planes at Zn atoms but [0001�] planes at O

atoms. Besides, the contrasting negativity on the top and bottom end of the unit cell also

induces a dipole moment along the c-axis, thus making ZnO piezoelectric.[1] When

stressed, the relative displacement between the Zn2+ and O2- planes changes the dipole

moment, hence screening charges to this dipole moment appear on the boundary of the

unit cell resulting in a measurable charge displacement known as the direct piezoelectric

effect. While when an electric field is applied, the dipole moment can respond by a

displacement of the Zn2+- and O2-- planes, hence a strain is observable in the unit cell,

which is known as converse piezoelectric effect.


7

Figure 2.2 Crystal structure of ZnO showing an unswitchable dipole moment due to alternating Zn2+ (black sphere) and O2- (grey sphere) planes[1]

The piezoelectric effect can be mathematically described by constitutive equations. In

the orthorhombic coordinate system, if the plan of isotropy is defined as the xy-plane,

then the poling direction can be defined as the z-axis, about which the material exhibits

symmetry.[8] The field variables are the stress components (Tij), strain components (Sij),

electric field components (Ek), and the electric displacement components (Dk). Hence,

the piezoelectric constitutive equation can be defined as:

Eij jkl i kl ijk kS s T d E (2.2.1)

Tk ijk kl ik kD d T E (2.2.2)

where s is the compliance constant, d is the piezoelectric constant, and ε is the dielectric

permittivity.[9-11] Equation (2.2.1) defines the converse piezoelectric effect of electric

field induced strain with the contribution of the material mechanical properties while

equation (2.2.2) defines the direct piezoelectric effect of strain induced charge


8

displacement with the contribution of the material capacitance. The piezoelectric

constant is identical in both converse and direct piezoelectric effect, which can be

expressed with a matrix by taking into consideration of the symmetries of transversely

isotropic material behaviour

15

15

31 31 33

0 0 0 0 0

0 0 0 0 0

0 0 0

d

d

d d d

(2.2.3)

where d31 is the transverse piezoelectric constant, d33 is the vertical piezoelectric

constant, and d15 is the sheer piezoelectric constant.[9-11] By combining the

constitutive equation with the piezoelectric constant matrix, the piezoelectric behaviour

can be mathematically described.

2.3 Pyroelectric Materials

The pre-fix pryo- means heat in Greek, hence pyroelectricity is a definition describing

that material can generate a charge displacement with respect to the change of

temperature. Crystals need to possess an intrinsic dipole moment to exhibit the

pyroelectricity, hence pyroelectric materials are all piezoelectric but piezoelectric

materials with non-polar crystal such as GaAs and quartz are not pyroelectric. ZnO,

which has an intrinsic dipole moment aligned with its c-axis, is a good example of

pyroelectric material.

Figure 2.3 is a schematic demonstration of the pyroelectric response with respect to a

change in temperature. The intrinsic dipole moment of a material with polar crystal

structure will generate a built-in electric field, which will be screened by space charges.

A change in temperature dT will accordingly induce a change in the polarization of the


9

material, and if the rate of change of temperature is higher than the screening rate of the

space charge, a potential can be generated until a new equilibrium is established. Within

this procedure, the charge flow can be observed in the external circuit to screen the

change in polarization, resulting in a current response with respect to dT. The

pyroelectric effect can be mathematically described as:

dP pdT (2.3.1)

where P is the polarization and p is the pyroelectric coefficient. Consider a time period

of dt, the pyroelectric current I can be described as:

dP AdTI p

dt dt (2.3.2)

where A is the electrode area. Upon heating the material, the pyroelectric response

becomes stronger as the temperature dependence of the polarization becomes stronger.

However, above the Curie temperature, a critical temperature defining the polar to non-

polar transition point, the pyroelectric response disappears as there is no dipole moment

in the material. This means that the pyroelectric materials should be used at

temperatures much below their Curie temperature. This results in pyroelectric

coefficients being lower, but less variable with ambient temperature as the dependence

of polarization on temperature is more linear at lower temperatures. The pyroelectric

effect originates from the temperature induced depolarization of oriented dipoles, of

which the procedure resembles that of the mechanical stress induced depolarization in

the piezoelectric effect. For instance, for a pyroelectric material with well oriented

dipole, a stress applied along the dipole orientation direction compresses the dipole and

can result in depolarization, while releasing the stress will cause the dipole to return to


10

its original status. This process will also induce screening charges to flow out or in,

which is analogous to the procedure in Figure 2.3. Due to this fact, all pyroelectric

materials are piezoelectric.

Figure 2.3 Illustration of the pyroelectric effect. An increase in temperature T reduces the spontaneous polarization Ps causing change in surface charge. This will induce a current flow to

composite the change in surface charge.[12]

2.4 Ferroelectric Materials

The concept of ferroelectricity is derived from that of ferromagnetism. In ferromagnetic

materials, the magnetic dipole moment is aligned to form a magnetic domain, which can

be polarized by the magnetic field. In ferroelectric materials, it is the electrical dipole

moment that forms the ferroelectric domain which can be reoriented by the electric field.

Hence, a material is ferroelectric when (i) the material possesses spontaneous

polarization and (ii) the spontaneous polarization is switchable with respect to the


11

electric field.[13] Hence, ferroelectric materials are a subset of pyroelectric materials.

Although ferroelectric domains comprise a set of dipole moments with the same

orientation, a polycrystalline ferroelectric material can possess large quantities of

randomly oriented domains, which cause the net dipole moment to be zero.[14] This is

to say, the spontaneous polarization is isotropic and the ferroelectric material has to be

polarized by an external electric field in order to exhibit piezoelectricity. Lead zirconate

titanite (Pb(ZrxTi1-x)O3) and barium titanate (BaTiO3) with perovskite ABO3 structure

are good examples of ferroelectric materials.

The crystal structure of BaTiO3 is illustrated in Figure 2.4. Ever since the discovery of

ferroelectricity in BaTiO3 in 1945, it has been one of the mostly studied materials.[15]

In the unit cell of BaTiO3, the Ba2+ ions occupy the A sites at the corners while Ti4+ is at

the body centre. The face centres of the unit cell are occupied by O2- ions, which form a

Ti-O octahedron. At high temperatures (above the Curie point), the crystal of BaTiO3

possesses a centrosymmetric cubic structure with no distortion in the Ti-O octahedron.

This results in zero dipole moment in the unit cell and the material is paraelectric. With

the decrease of temperature, the BaTiO3 crystal can be transferred from cubic to

tetragonal (373K), orthorhombic (278K), and rhombohedral (183K) structures, each

involving a small distortion to the Ti-O octahedron. These distortions can be regarded

as the elongation of the cubic unit cell along particular crystal orientations, which will

accordingly result in a relative displacement of the Ti4+ and O2- ions. This can induce a

net dipole moment in the unit cell, which give rise to the spontaneous polarization in the

ferroelectric phases of BaTiO3.


12

Figure 2.4 Schematic view of the structure of the different phases of BaTiO3. The Ba2+ ions (large sphere) are located at the corners, the Ti4+ ions (medium sphere) at the centre, and the O2- (small

sphere) ions at the face centres. The arrows show the polar direction along the cubic [001] direction for the tetragonal phase, the [011] direction for the orthorhombic phase, and the [111] direction for

the rhombohedral phase.[16]

Unlike ZnO whose spontaneous polarization is non-switchable, that in the BaTiO3

possesses a switching behaviour with the influence of electric field.[17] This makes

BaTiO3 not only pyroelectric, but also ferroelectric. By applying an external field, the

random oriented domains can be re-aligned to the field direction, which accordingly

induces a net dipole moment. If the field strength is stronger enough (larger than the

coercive field), these aligned dipole moment can be trapped after the unloading the

electric field and the ferroelectric material can exhibit piezoelectricity. This procedure is

named as polarization. P-E loops (polarization vs. electric field) are the most widely

used method to illustrate the ferroelectricity of a material. A conventional P-E loop for a


13

ferroelectric material after polarization saturation is shown in Figure 2.5.[18] The

ferroelectric behaviour can be described by the remnant polarization Pr and coercive

field Ec. While the Pr can represent the amount of trapped dipole upon unloading the

external field, the Ec represent the ability of a ferroelectric material to withstand the

external electric field without becoming depolarized. For a ferroelectric material with

randomly oriented dipoles, applying an external electric field stronger than Ec can

reoriented the dipoles along the electric field direction.

Figure 2.5 P-E hysteresis loop parameters for ferroelectric material[18]

In practise, a P-E loop is a D-E loop (charge displacement vs. field) as it is the charge

displacement D that is measured. D originates from the capacitance of the material,


14

which is a common response to electric field for all dielectrics and can be strongly

coupled with their leakage phenomena. Hence, it may led to false interpretations of the

material ferroelectric properties by solely use the P-E loop.[19,20] A more accurate

method to identify the material’s ferroelectricity is its I-E loop (current vs. electric field),

which is shown in Figure 2.6. Upon approaching saturation, current increases with

increasing E until EC is reached then decreases with further increasing E. This is

because fewer dipole moments can response to the electric field at saturation. Hence,

the distinct phenomena associating to the switching behaviour of a ferroelectric material

can be a current peak at Ec.


15

Figure 2.6 Electric displacement-electric field (D-E) loop measurement of NKN850 ceramics at 1Hz and 25°C. (a) Electric field versus time and current versus time (b) current-electric field (I-E)

hysteresis loop, (c) electric displacement-electric field (D-E) loop.[19]


16

Chapter 3 Poly(vinylidene fluoride) Ferroelectric Polymers

3.1 Conformational and Crystal Structure

The investigation of the molecular conformation of the PVDF polymer can be dated

back to the 1960s, when Wentink et al. firstly observed in their experiment that the

infrared spectra of PVDF change dramatically with temperature.[21] Albeit that no

explanation was given, their observations have attracted much attention to investigate

the conformational structure of the PVDF polymers. Theoretical calculation reported by

Liquori et al. indicates that more than one conformational structure exist in PVDF

polymer chains, which was later observed by Cortili et al. from infrared spectroscopy

(IR). [22,23] In their research, the PVDF sample films prepared from stretching after

casting were found to possess all-trans (TTTT) chains while those directly casted

without orientating treatment were found to possess trans-gauche (TGTG�) ones. Besides,

there is also a slightly defected form of TTTT conformation, which is found to be trans-

trans-trans-gauche (TTTGTTT G� ).[23,24] As PVDF is a crystallized polymer, the

packaging of molecule chains with different conformations can result in different crystal

forms, those are TGTG�-α, δ, TTTT-β, and TTTGTTTG�-γ.

The most commonly observed phase in the PVDF polymer is the α phase, which can be

attributed to its thermodynamic stability. The structure of α-PVDF is indicated in Figure

2.3.1. Early researches based on IR and XRD results have confirmed that the molecular

chain conformation of α-PVDF is trans-gauche (TGTG�), which is a chain conformation

without intermolecular dipole moment. Hasegawa et al. proposed that the α-PVDF

possess a pseudo orthorhombic unit cell with two TGTG chains packed in antiparallel

manner along the c-axis. The unit cell belongs to C2h point group with a lattice


17

parameter of a=4.96 Å, b=9.64 Å, and c=4.96 Å. Due to the antiparallel manner of the

chain package, no net intramolecular dipole moment will exist, hence the α-PVDF is a

non-polar phase and is paraelectric. There is also a modified form of α phase called δ

phase, which can be obtained by poling the α-PVDF at room temperature.[25] The

structure of δ-PVDF is also indicated in Figure 3.1. Davis et al. firstly proposed the

XRD spectrum of δ-PVDF by investigating the XRD and IR data, in which they

claimed that its unit cell parameter and molecular conformation is same as that of α

phase. However, changes in diffraction intensities can be observed in the δ-PVDF

spectra, which can be an evidence of a new chain packaging structure. Bachmann et al.

analysed the XRD data for δ-PVDF and proposed a statistical packing of the up and

down chains at the same site in the orthorhombic cell with the space group P21cn.

Unlike the α-PVDF, δ-PVDF is ferroelectric, in which the rotating of TGTG� chains

resulting in a net intramolecular dipole moment along the a-axis.


18

Figure 3.1 Molecular packing and crystal structure. (a), (b), Schematic packing of two polymer chains with the TGT�� configuration in the unit cell of the α-phase and the δ-phase. The symbols

present the in- and out-of-plane components of the dipole moment. In the α-phase all contributions cancel out. In the δ-phase the in-plane components cancel out but the out-of-plane ones yield a net microscopic dipole moment. (c), (d), The crystal structures and molecular packing of α-PVDF and δ-PVDF viewed along the c axis. The polymer chain is projected onto the ab-plane. (e), (f), Crystal

structure of α-PVDF and δ-PVDF viewed along the a axis. The drawn inner lines represent the unit cells. Grey circles represent carbon atoms, red circles fluorine atoms and blue circles hydrogen

atoms[25]

Lando et al. have conducted a XRD and NMR investigation in the crystal structure of β-

PVDF polymer, which was later refined by Hasegawa et al. by taking into consideration


19

of the CF2-CF2 steric hindrance.[26,27] The structure of β-PVDF is indicated in Figure

3.2, in comparison with that of α-PVDF. The unit cell of β-PVDF crystal was found to

be orthorhombic, which belong to point group C2v, with a unit cell parameter of a=8.58

Å, b=4.91 Å, and c=2.56 Å. The CH2-CF2 dipole in the in the TTTT chains cannot

cancel each other, resulting in a net dipole moment in the unit cell.

Figure 3.2 Comparison of the unit cell of the (a) α phase and (b) β phases. The yellow sphere is the carbon, the red sphere is fluorine, and the white sphere is hydrogen, (c) and (d) are the molecular

structure of α phase and β phase.[28]

The identification of γ-PVDF crystal have been confused for a long time. Based on the

IR results, Cortilli and Zerbi assumed that the γ phase might be a modified crystalline of

β phase with some extent of chain conformation disordering.[23,24] However, later

investigations have shown that the crystal structure of γ phase might be very different


20

from that of β phase.[29] Weinhold et al. proposed an orthorhombic unit cell with

a=4.97 Å, b=9.66 Å, and c=9.18 Å, in which two chains with a conformation of

TTTGTTTG� are packed.[30] The proposed structure is indicated in Figure 3.3. Almost

at the same time, Takahashi et al. reported that the unit cell could be monoclinic with

β=92.9°, and the cell parameter was found to be a=4.96 Å, b=9.58 Å, and c=9.23 Å,

with chain conformation and packaging same as Weinhold’s results.[31] The γ-PVDF as

an independent crystalline form with TTTGTTTG� conformation is finally approved by

Tashiro et al. by combined measurements of IR, Raman and wide-angle-XRD, which is

widely accepted nowadays.[32]

Figure 3.3 Molecular conformation and chain packing for γ-PVDF[30]

The crystal structure of PVDF can differs in samples processed at different conditions.

The relation between phase and processing condition is indicated in Figure 3.4.[33] For

instance, the solution-casted sample is a α phase when using non-polar solvents while

that can be a γ or β phase when using polar solvents. In terms of melting, the cooling

rate can play an important part as a normal cooling rate can always result in an α phase

while an extremely fast cooling rate can always induce a β phase. Interconversion

between phases in the as-prepared samples is also possible via specific treatments.


21

Mechanical stretching has been proved to be efficient in transferring α-PVDF into β-

PVDF.[34,35] Cakmak et al. have reported an α/β mixture in the melting spun PVDF

fibres, who claim that it might be the uniaxial stress that induced the formation of β

phase. Later observations have assured this point of view as more β phase is presented

in the stretched region compared with the non-stretched region and the transformation

procedure is stress dependent. The mechanisms concerning the stress induced phase

formation varies, including defects-assisting, molecular motion in the

crystalline/amorphous interphase, crystal reorganisation, and chain reorientation.

Electrical field is also capable to induce an in-situ α to β phase transition. Davis et al.

reported a that the α phase can be transferred to δ phase at moderate field strength or to

β phase at strong field strength.[36] More recent reports have shown that the direct

transfer from α to β phase is physically not possible due to the large energy barriers and

it is suggested that an α to γ to β transition route is more likely when an electric field is

applied. These results have shown that the ferroelectric β phase cannot be naturally

formed due to its relatively higher energy state over α phase, hence phase transition

from α to β have to grab energy from the external source such mechanical, electrical or

thermal energy in order to overcome the barriers.


22

Figure 3.4 Relation between PVDF phase and processing conditions, DMA is short for dimethylacetamide while HMPTA is short for hexamethylphosphoramide [33]

3.2 Ferroelectricity in PVDF Polymers

Ferroelectric materials are defined as material that possess spontaneous polarization

which is switchable by the electric field. As discussed above, β, γ, and δ-PVDF can all

be ferroelectric as they possess either intermolecular (β, γ) or intermolecular (δ) electric

dipoles. Herein in this section, we use the β phase as an example to introduce the

ferroelectricity in PVDF polymers.

As is well known that the polarization direction is aligned with the b-axis of the β-

PVDF unit cell, hence the switching behaviour can be monitored by the crystal structure

changes from a unpoled sample to a poled one. Early days observations of the

piezoelectric and pyroelectric responses of the PVDF polymer have led to two primarily

assumptions, with one being the trapped charge effect and the other being the

polarization switching. Kepler et al. studied the X-ray intensity of β-PVDF as a function

of sample orientation, in which a poling process can induce order in the orientation of


23

the crystalline regions.[37] This gives an evidence of the domain switching behaviour,

which indicates that the β-PVDF is ferroelectric. Also, in their research, the maximum

polarization P of the β-PVDF induced by a poling process is:

0

3P P

where P0 is the polarization in ideal conditions where all dipoles are perfectly aligned

with the electric field. Another demonstration of the switching behaviour of the β-PVDF

is done by Takahashi et al. who compared the intensity of the (110) planes by changing

the sign of the electric field. They found that the intensities of (110) under positive and

negative poling are different, hence if assign the crystal plane of positively poled β-

PVDF as [110], then that of negatively poled is then [1�1�0].[38]

3.3 PVDF Composites with Inorganic Inclusions

The most significant advantage of PVDF polymer is their highly insulation nature,

which result in a high dielectric strength. A pure PVDF polymer can possess a Ec over

200MV/m leading to a large discharging energy density, which can be attributed to its

highly insulating nature.[39-41] Hence, pure PVDF polymer is suitable in strong field

applications, particularly capacitors with high power output. While in the weak field,

their functionality can be hindered by the relatively weaker ferroelectric properties. Pure

PVDF polymer typically possess a relative dielectric permittivity from 8~19 (1kHz),

and a piezoelectric constant up to 50 pC/N (effective value measured in PVDF thin

film), which is far lower than their ceramic counterparts.[42,43] Therefore, alternative

routes that could effectively improve the ferroelectric properties of the PVDF polymers

is still an open question nowadays.


24

Introducing a heteroadditive into polymer matrix to form a 0-3 composite has long been

known as an efficient method to improve the properties of the pure polymer. For

example, Shah et al. have reported a dramatic enhancement in mechanical properties in

nanoclay filled PVDF polymers, where an increase of 0.5 GPa and 120% in elongation

was observed in comparison with the unfilled neat polymer.[44] Javadi et al. have

reported an enhanced strain energy density in chemically modified graphene/P(VDF-

TrFE-CFE) nanocomposite that is 4700 times larger than the pure polymer.[45] Li et al.

have reported an increase in conductivity in thermally reduced graphene/PVDF

nanocomposites, where a conductivity of 10-3 S/m was observed at a graphene content

of 0.105 vol.%.[46] The most widely studied aspect in PVDF composites is their

enhanced dielectric performance. In this section, we will use the dielectric performance

as an example to introduce the effect of inclusion additions.

A straight forward idea for boosting the dielectric response of a ferroelectric polymer is

to add ferroelectric ceramics with large permittivity to utilize the mixing effect. These

composites usually possess an inclusion volume fraction of 50 vol.% ~ 60vol.% and

dielectric permittivity significantly higher than that of the pure polymer. For instance,

Mao et al. managed to achieve a dielectric permittivity of 95 at 1kHz and BaTiO3

(100nm) of 60 vol.%, corresponding to 9 times increase over that of the pure PVDF.[47]

The major challenge in fabricating PVDF composites with ceramic inclusions is how to

avoid high leakage induced by Ohmic contact of agglomerated particles. Till now, the

most efficient route to address this issue is to coat a highly insulating polymer on the

ceramic particle surface to prevent direction charge transfer between adjacent

particles.[48,49] Figure 3.5 shows the polymer grafting process to coat the BaTiO3

surface reported by Yang et al.[48] In their research, BaTiO3 nanoparticles were first


25

functionalized by poly(1H,1H,2H,2H-heptadecafluorodecyl acrylate) (PHFDA) and

poly(trifluoroethyl acrylate) (PTFEA) via reversible addition-fragmentation chain

transfer (RAFT) technique before mixing and hot-pressing with poly(vinylidene

fluoride-co-hexafluoropropylene) (P(VDF-HFP)) polymer. The coating possesses

thickness from 2~6nm, which well isolates the BaTiO3 particles. Composites with 50

vol.% BaTiO3 of both coatings possess analogous dielectric permittivity around 45 at

1kHz, this results in a discharge energy density up to 4 times higher than the pure

P(VDF-HFP) (at 20kV/mm, 10Hz).

Figure 3.5 Schematic illustration for the preparation of fluoro-polymer@BaTiO3 nanoparticles and P(VDF-HFP) nanocomposite films[48]

The major drawback of using ceramic particles as an inclusion to enhance the composite

dielectric response is that a high solid loading is always needed. This increases the

fabrication difficulty as well as degrades the composite mechanical strength. An

attractive new candidate for hybridizing with ferroelectric polymers can be nano-sized

conductive particles such as carbon nanotube and graphene, which have been

demonstrated to induce a gigantic dielectric permittivity in composites with small solid


26

loadings.[50,51] Analogous to the ceramic fillers, pristine nano-carbons can also exhibit

poor dispersity in the PVDF solutions, therefore the polymerization technique is also

introduced to coating the nano-carbons.[52-54] Apart from this, there are also reports of

use the intrinsic oxidized form of nano-carbons and thermally or chemically reduced in-

situ in composite to retain its conductivity.[55-57] For instance, Tang et al. used an in-

situ thermal reduction technique to fabricate a rGO/PVDF nanocomposite, with

graphite-oxide (GO) as the raw inclusion.[57] The hydrophilic GO provides good

dispersity in PVDF casting solutions and can be thermally reduced in-situ to conductive

rGO, as shown in Figure 3.6. The dielectric permittivity and tanδ was found to be 662

and ~4 at 1kHz with merely 2.4 vol.% solid loadings, providing to be the best

combination reported. However, even with this promising dielectric figure, the energy

storage performance of composites with nano-carbons has not been widely reported.

Hence, how these high permittivity composites would behave at strong charging field

remains to be a question in this research scenario.

Figure 3.6 (a) Image of the graphene oxide and nanocomposite: (a) the in situ reduced process for the single layer reduced-graphene oxide nanocomposite, (b) digital image of graphene oxide and in

situ reduced-graphene oxide nanocomposite[57]

Mechanisms concerning the enhanced dielectric response in composite materials can be

classified into two categories: (i) the mixing rules dealing with the contribution of

inclusion dielectric permittivity and (ii) interfacial interaction model dealing with the

contribution of inclusion/matrix interface. The mixing rules include Lichtenecker’s


27

formula, Maxwell-Garnett equations, and Bruggemen approximation.[58]

Lichtenecker’s formula is the simplest form among those in mixing rules, which can be

expressed as:

log log (1 ) logm p cf f (3.3.1)

where εm, εp, and εc is the dielectric permittivity of composite, polymer and ceramic,

respectively, and f is the solid loading.[59] While Lichtenecker’s formula always lead to

large errors in practise, the Maxwell-Garnett and Bruggeman’s formula are more

commonly used. The Maxwell-Garnett model can be expressed as:[60,61]

2 ( )2

1

1 ( )2

c p

c p

m pc p

c p

f

f

(3.3.2)

while the Bruggeman’s formula can be expressed as:[62]

( )3 ( )

mm c p

m c p

f

(3.3.3)

The drawbacks of the mixing rules can be obvious, that the solid loading is regarded as

the only factor that dominates the dielectric response of the composites. Hence, the

mixing rules are not suitable to describe the size effect of the inclusions. Besides, the

mixing rules are more of a macroscopic approximation of the dielectric behaviour, and

the microscopic kinetics behind the dielectric response is still unclear. This means that

the mixing rules is insufficient to deal with the loss of the composites.

The addition of inclusion particles can induce massive interfaces, which give rise to the

interfacial interaction model, such as Lewi’s model and Tanaka’s model. These models


28

based on the assumption that an electric double layer or analogous structure should exist

on the inclusion surface giving rise to an improved dielectric in composites over the

matrix.[63-65] The static condition of an inclusion surface assumed by Lewi is sketched

in Figure 3.7.[63] The inclusion is regarded as a metallic, of which the surface is

assumed as negatively charged due to a Fermi level or electrochemical potential

difference between inclusion and matrix. The negatively charged inclusion surface can

absorb free charge carriers such as ions and molecules to construct an electrical double

layer (EDL) structure as sketched in Figure 3.7. The inner Helmholtz layer, which is

indicated as layer (c) in the figure, is the front layer of the EDL and is composed of

tightly bonded ions and highly ordered molecules. This inner Helmholtz layer is

followed by a less ordered outer Helmholtz layer (d) and a loosely bonded Gouy-

Chapman diffusion layer (e). The charge density δ(r) in the double layer with respect to

the distance away from the surface r, which can be described using Poisson-Boltzmann

relation as:

( )( ) exp( )

ze rr

kT

(3.3.4)

where δ∞ is the charge density in the bulk matrix, z is the valence, e=1.60×10-19C is the

electron charge, φ(r) potential gradient, k=1.38×10-23m2kgs-2K-1 is the Boltzmann

constant and T is the temperature in Kelvin. The length of the accumulation layer is

defined as the 1/κ where κ is the Debye-Huckel parameter with unit of m-1 as:[42]

2 22

m

e z n

kT

(3.3.5)


29

where εm is the dielectric permittivity of the matrix. With the definition of κ, the

potential gradient φ(r) can be described as:

0( ) exp( )r r (3.3.6)

where φ0 is the potential on the inclusion surface. These equations are also claimed to

be valid at the existence of an applied surface potential. The surface interaction model

indicates a strong charge polarization on the inclusion surface, which explains the

advantageous of inclusion particles with large surface area in contributing a large

dielectric permittivity to the composites. However, this model resembles the matrix as

an electrolyte with mobile charge carriers. As dielectric matrix is normally an insulator

with wide band gap, their electrical behaviour may be very different from an electrolyte.

Besides, only the properties of the matrix are considered with inclusions treated solely

as a charge blocking site. This fails to explain the variation between dielectric responses

for composites with conductive and non-conductive inclusions.


30

Figure 3.7 A metal electrode-dielectric interface showing (a), positive metal cores; (b), the outer electron cloud of the metal; (c), the structured inner Helmholtz layer of molecules and ions; (d), the outer Helmholtz layer and (e), the Gouy-Chapman diffuse space charge layer. The arrows indicate

the orientation of polar molecules, and the molecules at the inner Helmholtz layer are highly ordered compared to those at the diffusion layer. [63]

To discuss the mechanism of loss, Bowen et al. proposed an electric field concentration

model via finite element analysis (FEA) method, as shown in Figure 3.8. [66] In their

research, a matrix with relative dielectric permittivity εr=1 is divided to 50×50 squares.

An inclusion particle occupies a single square, with εr set to be 106 so that the field

distribution on the inclusion phase is 0. This means the inclusion particles are in

permanently breakdown status resembling conductors. The modelling results indicate

that the addition of inclusion always magnifies the applied field E, resulting in a local

field Elocal>E. Therefore, it is indicated that this field concentration contributes to an

improved effective dielectric permittivity to the composites. The field concentration is

found to be dependent on the inclusion volume fraction, with higher volume fraction

giving rise to a higher field concentration. Besides, the field concentration model also


31

deals with the dielectric strength of the composites. As the Elocal may be far stronger

than the E applied, the composites possessing a large ε may simultaneously possess

weaker Eb.

Figure 3.8 Finite element model of two phase composites with varying volume fraction of the conducting phase. Upper images show example random distributions of the conductor (gray) in a dielectric matrix (cyan), and lower images are corresponding contour plots after application of a normalized external electric field (Eapplied=1). For a filler-free matrix, Elocal=1 at all locations.[66]

3.4 β-Phase Formation in PVDF Composites

The addition of inclusions also affects the crystallization kinetics for the PVDF

polymers, as many researchers have observed a core-shell structure compromising a

layer of β phase crystal absorbed on the inclusion surface. Levi et al. reported an

enhancement in the piezo- and pyroelectric properties in CNT/PVDF composites and

claimed that this enhancement might be corelated to the increased β phase


32

crystallinity.[50] They claimed that the β phase might have some energetic relation with

the CNT surfaces as: (i) a layer of polymeric coating was observed on the CNT surface

and (ii) the β phase content is sensitive to the loading of CNT. Martins et al. obtained 90%

β phase in CoFe2O4/PVDF composites with a CoFe2O4 loading of 5 wt.%.[67] A core-

shell structure was also observed, and the coating layer was later assigned to be β-PVDF

with a face-on molecular orientation. Other researchers also reported a β phase

formation in PVDF composites with varies inclusion species.[68-70] These findings

indicate the β phase formation in PVDF composites is a universal phenomenon, which

causes many debates on the formation mechanisms.

The challenges of interpreting the inclusion induced β-PVDF formation mechanism can

be indicated from the example of a CNT/PVDF composites. Yu et al. studied the β

phase formation mechanism on the CNT interface with the help of density functional

theory (DFT) the model for simulation is illustrated in Figure 3.4.1 (a) to (h).[71] In

their results, they suggested that both TTTT and TGT�̅ chains can be absorbed on the

CNT surface, and the TTTT chain bonds more tightly on the CNT surface than the

TGT�̅ chain does. This indicates a confining effect of CNT surface, which is also

widely observed in other organic/inorganic type interfaces.[72-75]. Many assumptions

have been proposed to generate a molecular level explanation for this confining effect.

For instance, Manna et al. attributed the β phase formation on the CNT surface to the

matching of the zig-zag morphology between the PVDF chains and carbon atoms.[76]

While, Ke et al. fabricated a series of PVDF composites with surface functionalized

CNT, and attributed the formation of β phase to the chemical interactions between the -

CF2 or -CH2 and the functional groups.[77] Comparing these two reports, it is obvious


33

that CNT with both pristine and functionalized surface can induce a β-PVDF, which

means neither a morphological matching nor hydrogen bonding is mandatory.

Figure 3.9 Simulation model describing (a), (b) TGT�� and (c), (d) TTTT chains absorbed on the armchair CNT tube, (e), (f) TGT�� and (g), (h) TTTT chains absorbed on the zig-zag CNT tube[71]

On assumption that could potentially be universally explored concerning the inclusion

induced β-PVDF is the ion-dipole interaction model. Martins et al. studied the β phase

formation mechanism in PVDF 0-3 composites.[67] They fabricated the PVDF

composites with two kinds inclusions, those are NiFe2O4 and CoFe2O4, and found that

the β phase content in CoFe2O4/PVDF composite is much higher than that in

NiFe2O4/PVDF. By conducting a Zeta potential test for both inclusion particles, it was


34

found that the Zeta potential of CoFe2O4 is higher than that of the NiFe2O4, while the

potential value for both inclusions are negative. Based on this, it is claimed that the ion

on the inclusion surface causes an electrostatic field which interacts with the molecular

dipole inducing β-PVDF formation, as indicated in Figure 3.10. However, no direct

evidence of the β-PVDF dipole orientation is given in the research, hence the ion-dipole

interaction model is still not demonstrated. Besides, the charged state of the inclusion

surface may be different in the PVDF casting solution to that measured from Zeta

potential. These insufficiencies cast some doubt on the ion-dipole interaction model,

which means a universal mechanism concerning the inclusion induced β-PVDF

formation is still not well established.

Figure 3.10 Schematic representation of the interaction between CoFe2O4 nanoparticles and PVDF chains in the nanocomposite: the partially positive C–H bonds of the polymer are attracted by the

negatively charged ferrite surface due to the static electric force. This leads to the all-trans conformation of the polymer phase[67]


35

Chapter 4 Aim and Objectives

This project is concerned with a broad but systematic investigation of the role of

heterointerface in rGO/PVDF composite materials. The overall aim of this project is to

find the missing link between the interfacial electrical interaction and the structure and

ferroelectric properties of the composite materials. The ambition is thus to unify the

changes in structure and properties in the composite material with respect to the

inclusion addition to the interfacial electrical interactions. Several objectives have been

designed to achieve this goal, which are listed as follows:

To fabricate a group of PVDF nanocomposites with different volume fractions

of homogeneous dispersed reduced-graphite-oxide (rGO) via in-situ thermal

reduction technique as an example to study the interfacial interactions.

To establish a general model of the inclusion/matrix interface that highlights the

effect of electrical contrast and inclusion geometry on the dielectric behaviour,

those are dielectric response and loss, of the composites.

To investigate the energy storage behaviour of the rGO/PVDF nanocomposites

and discuss with the heterointerface model. To

To investigate the phase transformation phenomenon of PVDF polymer with

respect to rGO addition and discuss with the heterointerface model.

To fabricate piezoelectric devices with the rGO/PVDF nanocomposites, to study

the role of interfaces in the piezoelectric properties of these devices


36

Chapter 5 Experimental and Measurement Methods

5.1 Solution-casting of Pure PVDF film

The pure PVDF films were prepared via a solution-casting method. 2.5g PVDF powders

(Alfa Aesar, UK) were dissolved into 10mL N, N-dimethylformamide (DMF, ACS,

99.8%, Alfa Aesar, UK) solvent in a 50mL glass tube. The glass tube is then closed

with a plastic cap and sealed with tape, followed by magnetic stirring for 4h at room

temperature to fully break the agglomerations. The casting solution was then poured

onto a clean glass substrate and air dried overnight at room temperature. Then, the dried

PVDF films were peeled off from the substrates, sandwiched by alumina substrates,

transferred to the oven and thermally annealed at 100°C for 2h to completely remove

the residue solvents.

5.2 Solution-casting of the GO/PVDF Nanocomposites

Two kinds of carbon nanomaterials were chosen as the starting filler to fabricate the

nanocomposites, these are graphite oxide (GO) and commercial graphite nanoplate

(xGnP, Strem Chemistry, USA). The GO powders are generously provided by the

Surface Engineering Groups in University of Birmingham, which were fabricated via an

improved Hammer’s method. Briefly, graphite flakes with an average diameter of 45μm

(99.8% Alfa Aesar, UK) were mixed with KMnO4 at a weight ratio of 1:6 (3g/18g),

followed by infiltrating a H2SO4 (98%) and H3PO4 solvent mixture with a volume ratio

of 9:1 (360 ml/40 ml). The mixed suspension was then stirred for 12h at 50 °C on a

ceramic hotplate incorporating a magnetic stirrer. After cooling, the suspension was

poured into a beaker with 400 ml distilled water and 3 ml H2O2, and then centrifuged


37

several times to separate the GO powders. The separated GO was oven dried at 90°C for

24h and stored until required. To obtain a homogeneous dispersion, 0.1g GO and 0.1g

xGnP powders were dispersed into 10ml DMF solvents and sonicated for 12h before

use. The dispersibility of GO and xGnP in DMF solvents were compared after 4 days of

sedimentation as shown in Figure 5.1 (a) and (b). As indicated, the GO can provide

more stable dispersion compared to that of xGnP, as few residues can be observed on

the bottom of GO bottle. Hence, the GO dispersion is chosen for the following

experiment.

To improve the accuracy of GO content, 0.13g GO powder were dispersed in 10mL

DMF solvent to prepare the GO concentrated mixture. The mixture was then sonication

for 8h in a sealed glass tube. To prepare nanocomposites with GO content of 1.0 vol.%,

1.5 vol.%, 2.0 vol.%, and 2.5 vol.%, 2.5g PVDF powders were added to 0.45g, 0.68g,

0.92g, and 1.16g GO/DMF mixture and then magnetic stirred for 4h at room

temperature until no agglomerations present. The casting solution was then poured onto

a clean glass substrate and air dried overnight at room temperature. Then, the dried

GO/PVDF films were peeled off from the substrates, sandwiched by alumina substrates,

transferred to the oven and thermally annealed at 100°C for 2h to completely remove

the residual solvents.


38

Figure 5.1 Photograph comparing the dispersity of (a) GO and (b) xGnP in DMF solvents after sonication for 12h and 4 days of sedimentation

5.3 In-situ Thermal Reduction of the GO Particles

The GO/DMF mixture prepared from sonication method was poured into an alumina

boat and transferred into the oven to dry at 100°C overnight. The alumina boat with

dried GO particle was then closed with an alumina substrate and place in a tube furnace.

The GO particles were then rapidly heated in the tube furnace to 200°C and calcine for

1h in N2 atmosphere to simulate the in-situ reduction in polymer environment. The rGO

particles were then cooled down to room temperature and collected for measurements.

5.4 In-situ Thermal Reduction of the GO/PVDF Nanocomposites

The GO was transformed into electrically conductive rGO in a stepwise manner by

reduction in-situ in the PVDF polymer. The oven dried GO/PVDF nanocomposites

were sandwiched between alumina substrates and transferred to the oven to heat at

temperature of 120°C, 140°C, 150°C, 160°C, 170°C, 180°C, and 200°C for 1h. The

removal of functional groups in the GO powders changes the colour of the


39

nanocomposites from dark brown to black, as seen in Figure 5.2, which indicates a

narrowed bandgap in thermally annealed GO powders. Note also that the pure PVDF

film retains its natural colour when heat treated under the same conditions.

Figure 5.2 Photograph comparing the (A) PVDF film annealed at 200°C for 1h, (B) GO/PVDF film annealed at 100°C for 1h and (C) rGO/PVDF film annealed at 200°C for 1h

5.5 Lapping and Electrode-Sputtering the rGO/PVDF

Nanocomposites

The rough surface of the thermally annealed nanocomposites was polished to avoid

impact of surface roughness on the electrical properties. Briefly, the sample was cleaned

using ethanol and then waxed on a smooth glass substrate. The glass substrate with

sample was attached on a jig via vacuum and place on a glass lapping pan of a precision

lapping and polishing machine (PM6, Logitech Limited, UK). A mixture of 3μm


40

alumina particles, 1, 2-ethanediol (99.8%, Sigma Alderich, Germany), and water was

used as the lapping liquid. The lapping pan is running in 25r/min until the desired

thickness is reached. The lapped and polished samples were cut with a sharp knife into a

roughly 1cm*1cm squares. The samples were then sandwiched by a sample holder with

ϕ1mm round hole and placed in a sputter coater (KX575, Emitech, UK) and sputtered

with two cycles of Cr for 2min/cycle and one cycle of Au for 2min/cycle. This will

result in a Cr layer of 80nm and Au layer of 200nm. The Cr/Au electrode is also

sputtered on the other side of the samples.

5.6 Measurement Techniques

The microstructure of the GO, rGO particles as well as the cross-sectional morphology

of PVDF and nanocomposites were measured by scanning electron microscopy (SEM).

An SEM (FEI Inspect-F, Hillsboro, OR, USA) with acceleration voltage of 20kV and

spot size of 5 was used for measurements. The samples were pasted on the conductive

sample holder using adhesive carbon tape. Non-conductive sample such as PVDF and

nanocomposites were gold sputtered to improve the SEM image quality.

Fourier transformation infrared (FTIR) spectroscopy was used to measure the IR

absorption of the GO, rGO, PVDF, and composite samples. The IR spectroscopy based

on the theory that the chemical bonds absorb the IR radiation of its characteristic

frequency. Hence the structure of a molecule can be interpreted from its IR absorption

spectrum. An FTIR spectrometer (Tensor 27, Bruker Optik GmbH, Germany) with an

attenuated total reflection (ATR) accessory (Miricale, Piketech, USA) was used to

capture the IR spectra. A ZnSe crystal was used as the IR optic material. The incident

angle of the IR beam was 45°, of which the route is shown in Figure 5.3. Each sample


41

were measured with 32 scans and a resolution of 4cm-1. The wavenumber range was set

to 4000-600cm-1. The difference between ATR-IR technique and traditional FTIR is

that the detector the ATR-IR mode only measures the IR absorption in the reflected

beams rather than the transmitted ones. Hence, ATR-IR is suitable for the measurement

for non-transparent materials.

Figure 5.3 The route of IR beam in ATR-IR spectroscopy[78]

X-ray diffraction (XRD) was used to measure the phase present in the PVDF and

composite samples. According to the Bragg’s equation:

2 sinn d (5.4.1)

where n is the number of diffraction, λ is the wavelength of CuKα radiation, d is the

spacing of lattice planes, and θ is the diffraction angle. The diffraction peaks form a

pattern that is characteristic of the crystal structure of the sample. An X-ray diffractor


42

(Bruker D8 Advanced, Bruker, USA) with Cu/Kα as target (λ=1.5405 A). The sample-

under-test was fixed on the holder with the tube and detector rotates at rates of -1°/min

and +1°/min, respectively. The angle between the tube and detector is 2θ, which was set

to be 20° to 90° in this research.

The morphology as well as the local piezoelectricity was characterized via an atomic

force microscope (AFM) (NT-MDT, Russia) with a piezo-response (PFM) accessory.

The samples were glued on a conductive holder by silver paste and fixed on the AFM

stage. A Pt/Ir coated probe with a spring constant of 2.8N/m was used in contact mode

with the sample surface. A bunch of laser beam was focused on the backside of the

cantilever probe and reflected to a split photodiode detector. While scanning the sample

surface, the deflection of the cantilever probe will induce a displacement of reflected

laser spot on the detector, hence the fluctuation of the surface morphology can be

imaged. This is shown in Figure 5.4. As for the PFM, a DC bias VDC plus an AC voltage

VAC is applied from the probe to the sample, the corresponding piezoelectric amplitude

Г33 is:

33 33 33 cos( )DC ACd V d V t (5.4.2)

where ω is the angular frequency and ϕ is the phase angle indicating the domain

orientation.


43

Figure 5.4 Illustration of the AFM/PFM method, with the sample deforms to respond to the applied voltage [79,80]

The electrical parameters of a given material such as leakage current I0 and effect series

resistance Rs can be calculated from the I-V characteristics curves. In this research, the

I-V characteristic curves of the PVDF and nanocomposites were measured by a source

meter (Keithley 2400, Keithley, USA). The samples with ϕ1mm Cr/Au electrodes on

both surfaces was perpendicularly fixed on a glass substrate with epoxy and wired with

silver pasted. A voltage sweep from -50V to 50V to the sample was conducted via a

source meter (Keithley 2400, Tektronix, UK) and the corresponding current is also

measured by the source meter. The data is processed via a built-in I-V sweep program

(Tektronix, UK) in LabVIEW 9.0.

The dielectric behaviour of PVDF and the nanocomposites were measured by the

impedance method. An impedance analyser (HP4294a, Angilent Technology, USA)

with a customized fixer was used capture the impedance spectra. Before measuring the

sample, the testing system is calibrated at open circuit, short circuit, and with a resistive

load. The experiment was processed at room temperature and an excitation bias of

500mV was used. The testing range was between 50Hz to 50MHz.


44

The strong field dielectric performance of PVDF and the nanocomposites were

measured by a ferroelectric hysteresis tester (NPL, UK) composing of a function

generator, a voltage amplifier and a source meter. The ferroelectric hysteresis tester is

controlled by a LabVIEW 9.0 program. The samples with ϕ1mm Cr/Au electrodes on

both surfaces were clamped by two conductive tips in contact with the sample electrode

and fully immersed in silicon oil. An alternating voltage is applied through the voltage

amplifier to the sample and the current response I is captured by the source meter. The

charge displacement D within an individual period t1 to t2 is then defined as:

2

1

t

tD Idt (5.4.3)

In ferroelectrics, the dipole switching behaviour can dominate the dielectric response of

the material, hence the charge displacement D is also regarded as polarization P.


45

Chapter 6 Modelling the Dielectric Behaviour of a Composite

6.1 Introduction

It is well-known that the dielectric response of a composite is directly dependant on the

content and electrical properties of the inclusion material. The challenge is to establish a

model to describe the relation between dielectric behaviour of the composite and the

inclusion/matrix interaction. In this chapter, we will develop a model concerning the

dielectric behaviour that can be widely explored in composites with a wide selection of

inclusion species. As a composite always composes a matrix far more insulating than

the inclusion, it is possible to assume the inclusion is in a permanently percolated

condition. This simplifies a composite to a conductor/insulator diode, facilitating

modelling its dielectric behaviour using Schottky junction theory.

To accomplish this task, this chapter is organized as follows. We start from a

development of classic Schottky junction theory to describe the capacitance behaviour

of a conductor/insulator device. This theory will be applied to develop a model for the

dielectric behaviour of a conductor/insulator composite. Then, the structure and

morphology of the rGO particles and rGO/PVDF nanocomposites is studied. Finally,

the electric behaviour of the rGO/PVDF nanocomposites, such as the I-V and

impedance response, will be measured and discussed with the model.

6.2 Schottky Junction Theory and Device Capacitance

An intimate contact between metal and insulator can lead to two kinds of junctions,

ohmic junction or Schottky (rectifying) junction.[81] For Ohmic junction, there is no

energy barrier for charge flowing from insulator to metal or vice versa so that a linear


46

dependence of current I on voltage V can be expected. While for Schottky junction,

charges can flow freely in only one direction as a transfer barrier exists in the other.

This on-off characteristic makes the Schottky junction an important component in

heterostructure based devices.

Figure 6.1(a) shows the band diagram of a conductor and an insulator, with Ec is

referred to the bottom of the conduction bands while Ev is referred to the top of the

valence bands and E0 is the reference energy level of the free space. An important

concept in the band theory is the Fermi level EF which is defined by Fermi-Dirac

equation as:[82,83]

1( )

exp 1F

f EE E

kT

(6.2.1)

where f(E) is the probability of a particle possessing energy E, k is the Boltzmann

constant and T is temperature in Kelvin. At E=EF, f(E)=1/2, this defines the Fermi level

as a statistical concept that the probability of a particle possessing this energy is 50%.

At T=0K, f(E)=1, this also defines Fermi level as the top of the occupied levels at T=0

K.[84] The concept of Fermi level defines the carrier species and density for an

insulator material. A EF closer to Ec indicates the electron is the predominant carrier

while a EF closer to Ev indicates the hole is predominant. An intimate contact, defined

as contact without gap, between conductor and insulator will equalize their Fermi levels,

which will accordingly lead to a band distortion in the insulator as shown in Figure

6.1(b). This due to the charge transfer phenomenon where electrons are removed from

the high EF side and appear in the low EF side. The Fermi level position defined electron

(n) and hole (p) density on the junction surface can be described as:


47

exp( )c Fc

E En N

kT

(6.2.2)

exp( )F vp

E Ep N

kT

(6.2.3)

where Nc/Np is the effective density of states on the Ec/Ev, k is the Boltzmann constant,

and T is the temperature in Kelvin.[81,85] The difference between Ec and EF is the

Schottky barrier ΦB preventing reverse diffusion of electrons.

Figure 6.1 Electrical structure of a metal and a semiconductor (a) before contact and (b) after contact

A more relevant discussion to our research is the charge transfer phenomenon of a

Schottky junction with respect to the applied bias V. The most significant phenomenon

at the junction when V is applied is the shifting of EF. A reverse V applied through

insulator to metal always down-shifts the insulator EF due to electron extraction while a

forward V in turn up-shifts the insulator EF due to electron injection. Therefore,

equation (6.2.2) and (6.2.3) can be modified with respect to V as:

exp( )F vc

E E eVn N

kT

(6.2.4)


48

exp( )c Fp

E E eVp N

kT

(6.2.5)

Equation (6.2.4) and (6.2.5) describes a capacitive behaviour of the Schottky junction,

which means the junction can act as a charge blocking component for the

conductor/insulator device. The surface bias V also induce a charge limited current I at

the junction, which is defined as:

0 (exp( ) 1)eV

I IkT

(6.2.6)

where I0 is the diode leakage current, which is an intrinsic value to the insulator and is

defined as:

* 20

B

kTI AA T e

(6.2.7)

where A is the diode area and A* is the Richardson constant.[81,86] Equation (6.2.6) is

valid for both forward and reverse bias, which can be used to describe the rectifying

phenomenon of a Schottky diode device.

We now apply the Schottky junction theory to a more specific condition, an insulator

sandwiched by two pieces of conductor, which is known as MIM diode.[87] If the a thin

(≤10nm) insulator layer is considered, then a quantum tunnelling may occur which will

lead to a large current due to direct conductor to conductor travelling of charges.[88]

While, if a wide insulator layer is considered, then the direct tunnelling of charges can

be inhibited and the current is also a space charge limited current as described in

equation (6.2.6).[89] As the conductor/insulator/conductor structure resembles a

capacitor, the theory package of Schottky junction can be applied to study the capacitor


49

dielectric behaviours. Considering only electrons under a forward bias, the carrier

density change ΔN with respect to V can be described as:

0 exp 1eV

N NkT

(6.2.8)

where n=N0 is the Fermi level defined carrier density. Therefore, the charge density at

the junction is defined as:

0 exp 1eV

e N eNkT

(6.2.9)

This layer of negative charge in the insulator can form a Schottky capacitance C with

the mirrored positive charge on the conductor surface, which can be defined as:

0 exp 1AeNA eV

CV V kT

(6.2.10)

This equation bridges the gap between Schottky effect and the device capacitance,

which establishes the fundamentals for modelling the conductor/insulator composite.

6.3 Modelling of the rGO/PVDF heterointerface

The structure of a conductor/insulator composite can be described by the diode model

indicated in Figure 6.2(a). The diode is constructed by three identical metals (M1, M2,

M3) and an insulator (In) in intimate contact, and all junctions are assumed to be

Schottky junction. Regarding M1 as the system electrode, then M2 and M3 can resemble

the effect of inclusion particles. A bias V applied through M1 down-shifts the system

Fermi level causing electron to be extracted from the Insulator. Due to the equalization


50

of Fermi level, the bias V is simultaneously applied on the surface of M1, M2, and M3,

resulting in the device current I=I1+I2+I3, where

1 2 3 0 exp 1eV

I I I IkT

(6.3.1)

The magnified I by M2/In and M3/In indicates that the insertion of M2 and M3 can be

regarded as an effective expansion M1/In area. This cooperating manner indicates that

inclusion particles can enhance composite system capacitance by providing additional

charge blocking interfaces. This effect is shown in detail in Figure 6.2(b). Assuming a

composite capacitor possessing an electrode area A0, volume U, and inclusion volume

fraction f. The inclusion particles possess a total effective surface area A, which is

defined as the sum of surface area projected to the electrode surface. With the findings

in Figure 6.2(a), the composite resembles an equivalent capacitor with A+A0 as the

electrode area and (1-f)U/(A+A0) as capacitor thickness. Assuming A0<<A and f<<1,

which is the case for most high permittivity composites with nano-sized inclusions, the

electrode area of the equivalent capacitor can be simplified as A while the thickness as

U/A. This means for high permittivity composites, the dimension of inclusion particles

can have a predominantly impact on the system dielectric response.


51

Figure 6.2 (a) a diode model resembles a conductor/insulator type composite and (b) illustration for the effective expansion of composite system electrode by the addition of inclusion particles

We use the equivalent structure to study the dielectric behaviour of the

conductor/insulator composite. An alternating field is applied across the equivalent

structure resulting in a junction potential φ on the electrode, the C with respect to φ can

be derived from equation (6.2.10) as:

0 exp 1AeN e

CkT

(6.3.2)

Analogously, we could define the capacitance of a pure matrix with electrode area A0 as:

0 00 exp 1

A eN eC

kT

(6.3.3)


52

By comparing equation (6.5.3) and (6.5.4), we define the magnification coefficient υ as:

0 0

C A

C A (6.3.4)

The definition of υ demonstrates the origin of improved dielectric permittivity is the

expanded electrode area contributed by the formation of inclusion/matrix junctions. The

increase in the number of inclusion/matrix junctions lead to a higher A, hence the

inclusion volume fraction f can have a straightforward impact on the composite

dielectric response. However, the impact of f may not always be linear. Consider the

simplest form, a composite with identical spherical conductors, the effective junction

area A=nπr2 where n is the number of junctions and r is the sphere radius. In this case,

the increase in f could linearly increase the dielectric response. While for composites

with randomly dispersed platey conductors, the orientation angle may induce a non-

linear dependence of system dielectric response on f. Define the effective area of an

individual platey conductor as:

cosi iA S (6.3.5)

where Si is the area of the conductor and 0≤θ≤π, the total effective junction area A is

then:

1 1 2 2cos cos cosn nA S S S (6.3.6)

It is obvious that the set Sfncosθn is discrete, which means it could follow a normal

distribution if n is large enough. Therefore, we define the expectation of set Sncosθn as

Sexp, then equation (6.5.7) can be rewrite as:

expA nS (6.3.7)


53

Combining equation (6.3.6) and (6.3.7), it can be indicated that for composite with

isotropic inclusions, the increase of system dielectric response may be non-linear at

small inclusion volume fractions.

By understanding the origin of improved dielectric response, it is still important to

know that of loss to completely describe the dielectric figure of a composite. To start,

we show the electric field across the equivalent structure E* is given by:

*A

EU

(6.3.8)

E* represents the local electric field between the inclusion particles, hence equation

(6.3.8) indicates that the inclusions magnifying dielectric response can simultaneously

magnify the local electric field. This finding is analogous to the simulation results

reported in the literatures. [42,90-92] For an external field E, E*>E, which means the

strong field dielectric behaviour occurs at weaker field reducing the dielectric strength

of the composites. This initially explains the contradict between high dielectric response

and high dielectric strength. To describe the loss in detail, we studied the interaction

between adjacent inclusions as shown in Figure 6.3. According to the figure, we can

define a ω = �/2 as the critical depletion length where the spacing is fully populated by

charge carriers, the corresponding φ is then defined as critical potential φc. At φ<φc,

ω<1/2t which means depletion layers of M2/In and M3/In are well isolated by free space

and the device is an ideal capacitor. While at φ>φc, ω>1/2t would differentiates Ec in the

interference area as indicated by the dash line in Figure 6.3. This would populate the

interference area with carriers of mirrored charge hence induces a tendency for carriers

to recombine to re-establish equilibrium. Assuming the number density at φ is n(φ) and

that at φc is n(φc), their difference Δn = n(φ) − n(��) defines a pseudo-leakage to the


54

system due to the loss in carriers on the junction surface. As the system always retains

to the equilibrium after carrier recombination, its discharge energy Jd is then governed

by n(φc), which is:

1( )

2d c cJ Aen (6.3.9)

As energy efficiency η is defined as η=Jd/J where J=Jd+Jloss, the carrier recombination

induced pseudo-leakage can be described as:

1

( )exp

c

c c

en

kT

(6.3.10)

Equation (6.3.10) reveals an exponentially decay of η after carrier recombination

occurred, which also indicates it is insufficient to reduce the leakage by solely isolate

the inclusion particles.

Figure 6.3 Illustration of carrier recombination induced pseudo-leakage.


55

To sum up, our model suggests that composite capacitors can benefit from inclusion

particles with high surface area as they contribute to a large A. This accordingly grants

composite a high effective dielectric permittivity ε, which is in good agreement with the

experimental data reported in composite with graphene and carbon nanotube

particles.[51,57,93,94] However, inclusions with large surface area also increases the

matrix filling ratio,[92] which reduces the inter-inclusion spacing causing a smaller ωc.

This suggests composites with a higher ε are more likely to exhibit high loss and

possess a smaller dielectric strength.

6.4 Morphology and Structure of rGO and rGO/PVDF

Nanocomposites

In this section, we will characterize the microstructure of rGO particles and the

rGO/PVDF nanocomposites.

The structure of GO and rGO particles can be characterized by the XRD, which is

shown in Figure 6.4(c). The XRD results indicate a multilayer nature of individual GO

sheet with an interlayer spacing significantly increased from ~3.4Å of graphite to ~8.6Å

after oxidation, this is due to intercalated H2O molecules between GO lattice planes

after oxidation.[95,96]. Figure 6.4(b) and Figure 6.4(c) show the SEM image of GO and

rGO particles. The rGO particles were thermally reduced in N2 atmosphere at 200°C for

1h to simulate the in-situ reduction in polymer environment. Compared to the rGO

particles, the GO particles show stronger agglomeration due to large Van der Waals

force between surface functional groups. These results indicate the GO particles are

functional groups abundant, which may possess a good dispersity in the DMF solvent.


56

Figure 6.4 (a) X-ray diffractions for raw graphite and graphite-oxide prepared via Harmmer’s method, and Morphology of (b) GO particles and (c) rGO particles reduced at 200°C for 1h in N2

atmosphere

Figure 6.5(a) shows the ATR-IR spectra of the GO and TRGO, respectively, which

indicated the removal and reaction of varies functional groups. The GO spectrum was

contributed mostly by the O-H stretching (3050cm-1 to 3800cm-1) together with C=O

(1725cm-1), C-O-C (1160cm-1), and C-O (1080cm-1 and 1045cm-1), indicating the


57

existence of hydroxyl, ether, and carboxyl groups. [97-99] After thermal reduction at

200°C, the TRGO spectrum was carbonyl moieties dominated and differed from the

GO spectrum in that the broad peak at 3050cm-1 to 3800cm-1 was disappeared, which

was in accordance with the results observed in the literature. The difference between

GO and rGO spectrum indicated that while 200°C was sufficient to remove hydroxyl

groups, the carbon moieties will remain after reduction due to their increased thermal

stabilities. In addition, reactions between functional groups were observed. The peak at

1620cm-1 in GO spectrum represented the C=C stretching, which was shifted to

1540cm-1 after thermal reduction corresponding to the restoration of conjunctive

network of aromatic groups in the carbon backbones.[97,98] Moreover, ether group,

which was rarely found in GO, expanded in amount in rGO corresponding to the

increased intensity of 1160cm-1 peak due to the reaction between desorbed water and

carboxyl groups. Furthermore, the newly appeared peaks at 2980cm-1, 2880cm-1, and

1380cm-1 confirmed the formation of C-H bond served as defects on the carbon

backbones, which was a result of the removal of hydroxyl groups.


58

Figure 6.5 ATR-IR spectra for GO and rGO particles reduced at 200°C for 1h.

Figure 6.6(a) and (b) compare the cross-section structure of (a) an as-casted and (b) a

200°C reduced rGO/PVDF nanocomposite. Both samples were frozen at -18°C in a

freezer and broken by hand to avoid cutting scalps from affecting the morphology. As

for the as-casted sample, the cross-section morphology exhibits large roughness. This

could be a sign of high amorphous phase content in the as-casted sample causing high

plastic deformation at break. In comparison, the 200°C reduced sample cross-section

exhibits a brittle fracture which may indicate a high crystallinity. The bulk density of

200°C reduced sample were measured via Archimedes’ method and averaged between 3

samples, which was found to be 1.62 g/cm3 corresponding to 0.96 of the theoretical

value. Figure 6.6(c) shows the cross-section of a pure PVDF annealed at 200°C.

Analogous to the 200°C reduced nanocomposite sample, the pure PVDF annealed at

200°C also exhibits a brittle fracture. But the morphology is smoother for pure PVDF


59

compared to the 200°C reduced nanocomposite. This may be corelated to the addition

of rGO, which will be discussed in the following chapters.

Figure 6.6 (a) SEM image of (a) as-casted GO/PVDF nanocomposites, (b) rGO/PVDF nanocomposites reduced at 200°C for 1h, and (c) pure PVDF annealed at 200°C for 1h.

6.5 I-V Characteristics of the rGO/PVDF Nanocomposites

To demonstrate the effect of inclusion/matrix heterojunction, we measured the I-V

curves for a group of rGO/PVDF nanocomposite devices with varies of rGO content

and reduced at 200°C as well as a pure PVDF device. The nanocomposites used were


60

polished and sputtered with Φ1mm chrome/gold electrodes as described in Chapter 5. A

sourcemeter (Keithley 2400, Tektronix, UK) was used to sweep a voltage from -50V to

50V to the samples. The experimental data were collected via a Keithley built-in I-V

sweep program in Labview 9.0 (National Instrument, USA).

Figure 6.7(a) shows the I-V curves of PVDF and rGO/PVDF nanocomposites. To start,

the I increases with increasing rGO content. For devices with 2.0 vol.% and 2.5 vol.%

rGO (2.0-rGO@200 and 2.5-rGO@200), their I-V curves exhibit strong non-linearity.

These findings are good supports of the existence of a rGO/PVDF heterojunction.

Herein, we use the equation (6.2.6) to calculate the electrical parameters from the I-V

curves.[81,86] A two-diode series circuit can resemble the I-V response of the sample

device, which is shown in insert Figure 6.7(a). The diode 1 is in opposite connection

with diode 2, and therefore the overall current response of the system is limited by the

Schottky junction at diode1. As for a real device, the junction bias is smaller than that

applied due to the effective series resistance Rs contributed by contact, sheet resistance

and material dimensions.[100-102] Hence, equation (6.2.4) need to be modified as:[81]

0

( )(exp( ) 1)se V R I

I IkT

(6.4.1)

To estimate the Rs, we could use the high V section of the I-V curve where the

contribution of Rs to I could be dominant.[103] Similarly, we could also estimate the I0

from the high V section as at high V, -1 component of equation (6.4.1) could be

neglected and a simplified equation can be obtained:

0

( )ln ln se V R I

I IkT

(6.3.2)


61

The calculated results of Rs and I0 is summarized in Figure 6.7(b). As seen, the I0 is

4.1×10-9A in the pure PVDF device, which is in the same range as those in the 1.0-

rGO@200 and 1.5-rGO@200. With the rGO content increases to 2.0 vol.%, a sharp

increase of I0 to 4.8×10-7A was observed, followed with a further increase to 7.2×10-7A

in 2.5-rGO@200. As for the Rs, the value decreases with increasing rGO content, from

3.1×109Ω for the pure PVDF to 1.8×106Ω for the 2.5-rGO@200. The I0 is intrinsic to a

diode device as defined by equation (6.2.7), hence the only variable is the junction area

A. Due to this fact, it is reasonable to attribute the increase of I0 to the formation of

rGO/PVDF junctions. Meanwhile, the increased rGO content providing large junction

area also compacts the inter-rGO spacing, this lead to a decreased effective charge

tunnelling distance that causes the decreased Rs. Therefore, these findings are in good

agreement with the characteristics of the equivalent structure as shown in Figure 6.2,

which demonstrates the magnifying effect of rGO/PVDF heterojunction to the system

current response.


62

Figure 6.7 I-V curve of 50µm rGO/PVDF nanocomposites coated with φ1mm chrome/gold electrode with different rGO content, in comparison with a pure PVDF, the insert figure shows the

fitted results of I0 and Rs

6.6 Equivalent Circuit of the rGO/PVDF Nanocomposites

The impedance of a material resembles to that of its equivalent circuit. In this section,

the equivalent circuits of both pure PVDF and nanocomposites reduced at 200 °C were

measured. An impedance analyser (HP4295a, Agilent Technologies, USA) was used to

measure the impedance spectra, which is discussed in detail in Chapter 5. The

equivalent circuits were simulated from the impedance spectra by Zsimpwin software

(Ametek Scientific Instrument, USA).

Figure 6.8(a) shows the Nyquist plots of both pure PVDF and the nanocomposites. As

seen, the Nyquist plots exhibit the tendency to close a semi-circle at higher rGO content,

which is a sign of the increased impact of the charge transfer resistance Rct. As for the


63

pure PVDF device, we found its impedance response is identical to a single constant-

phase-element (Q), of which the impedance ZCPE is defined as:

1

( )CPE n

Zj Q

(6.3.1)

where n is a factor between 0 (resistor) and 1 (capacitor), ω is the angular frequency and,

and Q is associated to the CPE capacitance.[104] Contrasted to the pure PVDF, we

found it is only by assuming a parallel circuit that can the electrical behaviour of the

nanocomposites can be reasonably described. As seen, the Q2 is in series connection

with Rct and then connected with Q1 in parallel, this means the Rct-Q2 controls the

system charge transfer kinetics. The fitting results of the equivalent circuits attribute the

introduction of the Rct-Q2 component to the addition of rGO particles, which is listed in

Table 6.6.1. To start, Q2 is larger than Q1 and is increasing with rGO volume fraction.

This indicates a predominant contribution of Q2 to the system capacitance, and the

capacitance increases with increasing rGO content. Meanwhile, comparing to the

quality factor n1 of Q1, the n2 for Q2 exhibits smaller values, and is decreasing with

increasing rGO content. This means the Q2 component resembles more to a resistor

device with increasing rGO content. Therefore, if assigning the Q2 as the rGO/PVDF

heterojunction capacitance, its characteristics with the rGO content are in good

agreement with the equivalent structure model in Figure 6.2(b). Combining the results

calculated from the I-V curves, we claim the inclusion/matrix heterostructure would

dominate the system capacitance of a composites, and the equivalent structure indicated

in Figure 6.2(b) can be used in the following sections to study the dielectric behaviour

of the rGO/PVDF nanocomposites.


64

Figure 6.8 Nyquist plot of pure PVDF and rGO/PVDF nanocomposites, and their corresponding equivalent circuits

Table 6.6.1 Equivalent circuit parameters for pure PVDF and nanocomposites

Sample Geometry Q1 (S·sn) n1 Q2 (S·sn) n2

PVDF Φ1mm*40µm 0.47*10-11 0.94 - -

1.0-rGO@200 Φ1mm*40µm 1.74*10-11 1 5.80*10-10 0.76

1.5-rGO@200 Φ1mm*40µm 0.84*10-11 1 4.38*10-10 0.74

2.0-rGO@200 Φ1mm*40µm 1.42*10-11 1 3.12*10-9 0.68

2.5-rGO@200 Φ1mm*40µm 2.12*10-11 1 1.5*10-8 0.62


65

6.7 Summary

In this chapter, we proposed a model describing the effect of inclusion/matrix

heterojunction on the composite dielectric behaviours. This model is partially discussed

with the experimental data measured from both pure PVDF and rGO/PVDF

nanocomposites. The findings of this chapter can be summarized as the followings:

1. We suggest the effect of adding inclusion particles as an effective expansion of

the electrode area for a composite capacitor device, which explains the improved

dielectric response. Besides, we also suggest the carrier recombination between

the adjacent inclusion/matrix junctions contributing predominantly to the loss of

the composite capacitor.

2. We show the carrier recombination kinetics define a charge density limited

discharge energy Jd to the composite device, which indicate the device energy

density decreases exponentially with increasing charging field after

recombination occurred.

3. We measured the I-V curves as well as impedance spectra of the rGO/PVDF

nanocomposites, in comparison with those of a pure PVDF device. These results

showed evidences of the existence of the rGO/PVDF heterojunction, which can

be good supports to our model.


66

Chapter 7 Dielectric Behaviour of the rGO/PVDF

Nanocomposites

7.1 Introduction

In the last chapter, we have shown good support to the mechanism of inclusion/matrix

heterojunctions contributing predominantly to the composite dielectric response.

However, there is still a lack of evidence for the charge carrier recombination induced

loss. In this chapter, we will measure the dielectric behaviour of the rGO/PVDF

nanocomposites and discussed with the model proposed in the last chapter.

This chapter is structured as follows. To begin with, we show the impact of both

reduction temperature and rGO content on the dielectric permittivity of the

nanocomposites by investigating their properties in the frequency domains. After that,

we measured the discharging energy density Jd of the nanocomposites via ferroelectric

hysteresis test. The charge carrier recombination induced loss is evidenced by studying

the nanocomposite hysteresis loops. By understanding the kinetics of charge storage and

loss, we established an explicit relation between composite dielectric permittivity and

its discharge energy density. This for the first time makes it possible to design large

energy density composite capacitors via tailoring their dielectric responses.

7.2 Dielectric Responses of the rGO/PVDF Nanocomposites

In this section, we investigate the frequency domain of the dielectric permittivity and

tanδ of the nanocomposites. The nanocomposite films were polished as described in

Chapter 5 and sputtered with ϕ1mm Cr/Au electrode. The frequency domain of the


67

dielectric response is measured by an impedance analyser (HP-4294a, Agilent

technology, USA) with a sinusoidal excitation bias level of 500 mV.

Figure 7.1(a) shows the frequency domain of the relative dielectric permittivity εr of

1.5-rGO reduced at different temperatures. As seen, while the reduction temperature can

have an observable impact on the εr of the nanocomposites, the effect is not linear. For

instance, the εr@1kHz is measured to be around 17 and barely changed between 100 °C

and 140 °C, which is almost identical to that of the pure PVDF. Measurable difference

of the εr is observed for samples reduced above 140 °C, after which the εr is increased

significantly with increasing temperatures. As seen, the εr for 1.5-rGO@150 is 20,

which is increased stepwisely to 50 for 1.5-rGO@200. Figure 7.1(b) shows the

frequency domain of tanδ at different annealing temperatures for 1.5-rGO. tanδ is

defined as the ratio between imaginary and real part of the permittivity and hence is

representing the loss of the nanocomposites. Analogous to that of the εr, the tanδ only

increases at above 140 °C, which indicates a more lossy behaviour for the

nanocomposites reduced at higher temperatures. Generally, the tanδ@1kHz is always

attributed to the conduction due to travelling charges. While as seen in Figure 7.1(b), a

Debye term peak emerges at above 140°C, which can be assigned to the relaxation

phenomenon of the nanocomposites. This means the conduction loss might be coupled

with the relaxation phenomenon and thus tanδ@1kHz cannot be merely assigned to the

leakage of the nanocomposites. Herein, we could correlate the temperature dependence

of the dielectric behaviour to the change in effective series resistance Rs of the

rGO/PVDF heterojunction. As discussed in Chapter 5, the reduction of rGO can be

classified into 2 stages, namely (I) removal of H2O molecule at T ≤ 140°C and (II)

major removal of oxygen containing group at above 140 °C.[105] As reported, the


68

electrical structure of rGO is closely related to its C/O ratio, and a major removal of

functional groups at above 140 °C can lead to a sharp decrease in the C/O and therefore

a more metallic behaviour due to the restoration of the sp2 bonding networks.[106-110]

This leads to a higher capacitance via reducing the Rs on the rGO/PVDF heterojunction.

Figure 7.1 Frequency domain of (a) relative dielectric permittivity and (b) tanδ of 0.015-rGO-PVDF nanocomposites reduced at the temperature range from 100°C to 200°C for 1h


69

Figure 7.2(a) shows the frequency domain of the εr of the nanocomposites reduced at

200°C with respect to the rGO content f. As expected, the εr increases with increasing f.

For instance, at the εr@1kHz was measured to be 22 for 1.0-rGO@200, which was

increased to 380 at for 2.5-rGO@200. This is a significant increase in εr over that of the

pure PVDF, for which the εr@1kHz was measured to be 11. Figure 7.2(b) shows the

frequency domain of tanδ of the nanocomposites with respect to the f. Albeit higher

than that of the pure PVDF, the tanδ@1kHz is merely 0.3 for 2.5-rGO@200, compared

to that of 0.2 for 1.0-rGO@200. Regarding to the εr value as high as 380, the

tanδ@1kHz observed in this research is significantly lower than those usually reported

(tanδ@1kHz ≥1).[45,51,54,56,111-113] The relation between tanδ and f is defined by

the percolation theory as:

tan ( )acf f (7.2.1)

where fc defining the percolation threshold and a is a constant.[114] According to

equation (7.2.1), the weak dependence of tanδ on f indicate the rGO content is still away

from the percolation threshold. Therefore, it is reasonable to regard the dispersion of

rGO as homogeneous.


70

Figure 7.2 Frequency domain of (a) relative dielectric permittivity and (b) tanδ of rGO-PVDF nanocomposites reduced at 200°C for 1h

7.3 Energy Storage Performances of the rGO/PVDF

Nanocomposites

In Chapter 6, we suggested composite capacitors possessing higher ε are more likely to

exhibit high loss on charging the devices. This has, however, still not been approved by


71

the experimental data nowadays as there is few reports about the energy storage

performance for high ε composites. To discuss with the model in Chapter 6, we

calculated the discharge energy density and energy efficiency of the rGO/PVDF

nanocomposites by measuring their charge displacement vs. electric field (D-E) loops.

Figure 7.3(a) shows the calculated discharging energy density Jd of the nanocomposites,

which is calculated as:

21

2dJ E (7.3.1)

where η is the energy efficiency and E is the charging field. As indicated, the

nanocomposites can possess an enhanced Jd compared to the pure PVDF at weak field.

For instance, the Jd of 1.0-rGO@200 is calculated to be 0.002J/cm3 at 4MV/m, which

was increased to 0.012J/cm3 in 1.5-rGO@200, corresponding to 4 and 24 times

increased over pure PVDF under the same field strength. We found the problems

preventing nanocomposite capacitors from achieving higher Jd are: (i) too weak

dielectric strength Eb, and (ii) rapidly decreasing energy efficiency η. These problems

are indicated in detail in Figure 7.3(b) and (c), respectively. Figure 7.3(b) shows the Eb

of the nanocomposites defining the maximum charging field of a capacitor. It can be

indicated that the addition of rGO decreases the Eb. The pure PVDF is very tolerable to

the external field due to its highly insulating nature, and the Eb was found to be

220MV/m in this research. With the addition of rGO, the Eb dropped dramatically to

34MV/m for 1.0-rGO@200, which is 6 times lower than that of the pure polymer.

Continuing increasing the f results in an even more reduced Eb. For instance, the Eb for

the 2.5-rGO@200 is merely 3MV/m. The weak Eb prohibits a large charging field


72

strength overshadows the high ε merit of the nanocomposites. Figure 7.3(c) shows the

energy efficiency of the nanocomposites, which is defined as:

dJ

J (7.3.2)

where J is the theoretical energy density. Analogous to that of Eb, the addition of rGO

can dramatically decrease the η. For instance, the η of PVDF at 1kV/mm was 0.98,

which decreased to 0.69 in 1.0-rGO@200 and further to merely 0.04 in 2.5-rGO@200.

Besides, the η shows a strong field strength dependence. Comparing to the pure PVDF

exhibiting a linear η drop, that of the nanocomposites (except 1.0-rGO@200) decreases

more rapidly in an exponential manner with increasing charging field. According to the

model proposed in Chapter 6, the relation between η and E can be described as:

1

expgate

gate

E E

b E E E

(7.3.3)

where b is a constant and Egate is the critical field when charge carrier recombination

occurs. This equation can be partially approved by the exponential decay of η with

increasing E in Figure 7.3(b), which supports the carrier recombination kinetics in

contributing to the leakage. The energy storage performance measured in this section

provides an experimental demonstration for the correspondence of high ε and high loss,

which means high ε composite are not practically suitable for large energy density

applications.


73

Figure 7.3 (a) discharging energy density Jd, (b) dielectric strength, and (c) efficiency η vs. field strength E for nanocomposites reduced at 200°C with varies of rGO content

The carrier recombination phenomenon can be directly evidenced from the D-E (charge

displacement vs. charging field) loops of the nanocomposites. (1.5-rGO@200), as

shown in Figure 7.4(a) shows the D-E loops of the 1.5-rGO@200 measured at 1 MV/m,

5 MV/m, and 8 MV/m. As seen, on charging the device at 1MV/m 10Hz, the device

exhibits a classic capacitor D-E loop with η=0.65. While on charging the device at 5

MV/m, the D-E loop become flatter with an overcharging section exist on the discharge

section. This overcharging phenomenon is enhanced when increasing the charging field

to 8 MV/m, resulting in a drop in η from 0.11 (5 MV/m) to 0.02. The overcharging

phenomenon was found as electric-field-gated, and the Egate was found to be 2 MV/m.

This gating characteristic corresponds to equation (7.3.3), which is an indicator of


74

carrier recombination. The relation between overcharging and carrier recombination is

illustrated in detail in Figure 7.4(b). When � < ��, potential on rGO/PVDF junction

�� < �� hence no carrier recombination occurs. This resembles charging the device at

1MV/m, with only the ballistically transporting or hopping free carriers contribute to the

leakage. When � > ��, �� > �� triggering carrier recombination result in a loss of

carrier Δn1 on the junction surface. On discharging the device, potential drops to φ2

where �� > �� . This will resupply a carrier density of Δn2 to be recombined until

potential drops to φc. This resupply of charge carriers resembles a pseudo-charging

conduct, hence contributes to the overcharging curve on the D-E loop. The overcharging

curve defines the flatness of the device D-E loops causing a sharp drop in η,

demonstrating the carrier recombination as a predominant contributor to the leakage of

composite capacitor devices.


75

Figure 7.4 (a) D-E loops of 1.5-rGO@200 showing field-gated leakage and carrier recombination induced overcharging effect, and (b) band distortion between rGO particles illustrating the kinetics

of carrier recombination

7.4 Modifying the rGO/PVDF Heterojunction for Achieving Large

Discharge Energy Density

The carrier recombination kinetics also opens a new route for achieving large energy

density in composite capacitors. According to the last section, an increase in ε would

simultaneously decrease Eb, therefore a possible strategy one can use to avoid an early

breakdown is to reduce the composite ε to increase Eb. However, a significant decrease

in ε will in turn degrade the dielectric behaviour of a composite to its matrix. This

means further study to balance the ε and Eb is still needed.


76

Fortunately, the temperature tuneable structure of rGO offers us the opportunity to study

the ε-Eb relation. As indicated in section 7.2, the dielectric response of the rGO/PVDF

nanocomposites is smaller when reduced at lower temperatures, it is interesting to know

how these lower temperature reduced nanocomposites can behave at strong charging

field. Figure 7.5 shows the D-E hysteresis loops of the 0.015-rGO nanocomposites

reduced at a temperature range from 100°C to 200°C. As seen, increases in D was

observed in 1.5-rGO@150 and 1.5-rGO@160, which is measured to be 1.7 µC/cm2 and

4.1 µC/cm2, respectively. These results show the enhancement over 1.2 µC/cm2 of the

pure PVDF. Besides, the overcharging phenomenon is not observed when charging the

at 50 MV/m and the samples show relatively slimmer hysteresis at stronger electric field

compared to that of 200°C reduced.

Figure 7.5 D-E hysteresis loops measured at 50MV/m at 10Hz for 1.5-rGO nanocomposites reduced in the temperature range between 100°C and 160°C


77

The enhanced energy storage performances of the nanocomposites reduced at lower

temperatures are shown in Figure 7.6(a), (b), and (c). To begin with, a dramatically

enhanced dielectric strength was observed, which is plotted in Figure 7.6(a). For

instance, the dielectric strength of 150 °C and 160 °C reduced nanocomposites are 145

MV/m and 70 MV/m, respectively, compared to that of merely 9 MV/m in composite

reduced at 200 °C. This enhancement in Eb prolonged the upper limit of the charging

field strength, and a Jd is achievable in nanocomposites reduced at lower temperatures.

The Jd and η of the 1.5-rGO@150, 1.5-rGO@160 and a pure PVDF are calculated and

shown in Figure 7.5(b) and (c). Herein, the η=0.5 was set as the cut-off efficiency. As

expected, nanocomposites reduced at lower temperatures can exhibit a higher η. For

instance, the η of 1.5-rGO@200 is 0.65 at 1 MV/m, in significant contrast to that of 1.5-

rGO@150 and 1.5-rGO@160, which is 0.94 and 0.92 at 10 MV/m, respectively. The

reduced loss has led to a more promising Jd. For instance, the Jd of 1.5-rGO@160 is

0.67J/cm3 at 50MV/m, which is 3 times of that of pure PVDF measured at same

condition.


78

Figure 7.6 Effect of reduction temperature on the (a) dielectric strength, (b) discharging energy density Jd and (c) efficiency η of 0.015-rGO

7.5 Relation Between Dielectric Permittivity and Discharge Energy

Density

The above discussion about ε and Jd makes the question about how to design the

composite ε particularly important. The challenge to answer this question is to establish

a method of using ε to evaluate the discharge energy density Jd of a composite at any

charging field.

As discussed, the carrier recombination is charge density limited, which may indicate a

direct relation between η and charge displacement D. To demonstrate, we plotted a


79

series of discrete η-D pairs in Figure 7.7, which were measured from a pure PVDF and

all nanocomposites involved. We show the η-D relation of all samples can be described

by an exponential decay function, which can be constructed as:

0 expD

(7.5.1)

where �� = 1 is the static energy efficiency and α is a constant. By fitting with only the

experimental data of the PVDF, we found α=0.051, and the function is shown as a solid

curve in Figure 7.7. As seen, the curve is also in good agreement with experiment data

of the nanocomposites, demonstrating the η-D relation is intrinsic to the matrix

regardless of the conditions of inclusion particles. Using � = ��, equation (7.5.1) can

be modified to:

, exp0.051

EE

(7.5.2)

Equation (7.5.2) establishes the η-ε relation making possible evaluating Jd for PVDF

composite at any charging field by calculating the corresponding η by ε. As an example,

the insert figure in Figure 7.7 compares the experimental and calculated Jd for 1.5-

rGO@150 and 1.5-rGO@160. As seen, the calculated Jd curves fit reasonably well with

the experimental data, though an underestimation is observed at stronger charging field.

The gap between calculation and experiment can be attributed to the non-linear junction

capacitance as well as the instantaneous conformational transition of PVDF

polymers.[115] Therefore in practise, we claim equation (7.5.2) is relatively accurate in

evaluating Jd for composite capacitors charging at weak field or constructed with a


80

linear matrix. For those charging at strong field or constructed with a non-linear matrix,

equation (7.5.2) may only estimate the lower limit of their Jd.

Figure 7.7 Plots of discrete efficiency-charge displacement pairs measured from both pure PVDF and nanocomposite devices with varies reduction temperature and rGO content, the solid curve is the fitting result of the PVDF device, which fits well with the nanocomposites data, insert figure

compares the experimental and calculated discharge energy density for two nanocomposite devices.

7.6 Summary

In this chapter, we measured the dielectric behaviour of the rGO/PVDF nanocomposites,

the results demonstrate the model in Chapter 6. The findings of this chapter can be

listed as the followings:

1. Enhanced dielectric permittivity has been observed in rGO/PVDF

nanocomposites. The dielectric permittivity is found to be affected by two

factors, the rGO volume fraction and reduction temperature. This demonstrates

the contribution of rGO/PVDF heterojunctions.


81

2. We demonstrate composites with higher dielectric permittivity are more likely to

exhibit high loss. The high dielectric permittivity can inevitably cause a weak

breakdown strength, and their energy efficiency drops more rapidly upon

increasing the charging field strength. This finding implies that tanδ is not a

suitable parameter to evaluate the loss of composite capacitors.

3. We demonstrate the charge carrier recombination as the predominant kinetics of

leakage in composite capacitors with large dielectric permittivity.

4. We show a strategy to improve the discharge energy density by balancing the

dielectric permittivity and dielectric strength of the composites. This done by

increasing the series resistance of rGO/PVDF heterojunction via a low

temperature reduction regime. A nanocomposite with 1.5 vol.% rGO reduced at

160°C exhibits a discharge energy density of 0.67 J/cm3 at 50MV/m, which is 3

times higher than that of the pure PVDF.

5. We established an explicit relation between dielectric permittivity and energy

efficiency, which can be used to predict the discharge energy density of a

composite capacitor.


82

Chapter 8 β-Phase Formation in the rGO/PVDF

Nanocomposites

8.1 Introduction

There are three conformations in PVDF molecule chains resulting at least 4 distinct

crystal structures. Among those, β phase is the most desired in smart device applications

as it exhibits the strongest dipole moment. One of the dramatic effect of inclusion

addition is to induce β phase nucleation in PVDF polymer. This makes the PVDF

composite ferroelectric and applicable to smart devices. This chapter is an investigation

of the β phase formation in rGO/PVDF nanocomposites. The purpose of this chapter is

to reveal the characteristics of β phase crystal in the rGO/PVDF nanocomposites to

show their applicational potential in smart devices.

To do this, this chapter is structured as follows. First, we will study the molecular

conformation in rGO/PVDF nanocomposites using the attenuated total reflection

infrared (ATR-IR) technique. Both effects of reduction temperature and rGO content are

investigated. Then, we report a detailed investigation of the crystal structure by the X-

ray diffraction (XRD) technique. The morphology and local piezoelectric response of

the nanocomposites will be measured by the Atomic-/Piezo-force microscopy

(AFM/PFM). These results are discussed and a mechanism for β phase formation is

proposed with consideration of the contribution of the rGO/PVDF interface.


83

8.2 Molecular Conformation in the rGO/PVDF Nanocomposites

In this section, we report the use of infrared (IR) absorption spectra to investigate the

molecular conformation in the rGO/PVDF nanocomposites. rGO/PVDF

nanocomposites with rGO content between 1.0 vol.% to 2.5 vol.% and reduced at 100°C

to 200°C for 1h were prepared and tested. An FT-IR spectroscopy (Tensor II, Buker

Cooperation, Germany) with a single reflection ATR accessory (MIricale, Piketech,

USA) was used, details can be found in Chapter 5.

Figure 8.1 shows the ATR-IR spectra for the rGO/PVDF nanocomposites and pure

PVDF, all of which were annealed at 200°C for 1h. For the pure PVDF polymer, sharp

peaks at 614 cm-1, 760 cm-1, and 976 cm-1 was observed, which can be associated to the

non-polar TGT�̅ molecular conformation.[116] Meanwhile, the much stronger peak at

1271 cm-1 compared to 840 cm-1 and the absence of peaks at 813 cm-1, 1234 cm-1, and

1275 cm-1 indicated that the α phase is predominant in the pure PVDF.[29,32,117] This

can be attributed to the thermal stability of α phase that resulting in a preferred

nucleation. While for the nanocomposites, the newly emerged peaks as well as intensity

changes were observed in the IR spectra, which can be associated to the formation of

TTTT conformations. To start, the 614 cm-1, 764 cm-1, and 976 cm-1 bands can still be

observed, which indicates the existence of TGT �̅ chains in the nanocomposites.

Meanwhile, an increased relative intensity of the 840 cm-1 band over the 1271 cm-1 band

was observed, which can be associated with the formation of long term (T>3) trans

sequence and could be recognized as the characteristic of β phase. In addition, two

shoulders peaks were observed at 813 cm-1 and 1230 cm-1, which could either be

attributed to the existence of γ phase with shorter trans (T<3) sequence.[23] Because the


84

absorption bands of γ phase exhibits as shoulder peaks with weak intensity, we therefore

treat the shorter trans sequence as the defect in TTTT chains. According to the IR

spectra, we claim the addition of rGO can induce the transition of TTTT PVDF chains

that constructs the β phase.

Figure 8.1 ATR-IR spectra of pure PVDF and rGO/PVDF nanocomposites

The relationship between the formation of β phase and the annealing temperature Tr is

shown in Figure 8.2 The results indicate that while pure PVDF and the nanocomposites

show analogous phase content when annealed at low temperatures, variations can be

observed at annealing temperatures of 200°C. Figure 8.1 (a) shows the ATR-IR spectra

for pure PVDF polymer annealed at 100°C, 150°C, 170°C and 200°C for 1h. For pure

PVDF annealed at 100°C (PVDF@100), the relative high intensity of 840 cm-1 can be

attributed to the existence of all-trans conformations of polar phase, and the relatively

higher intensity of 1230 cm-1 over that of 1271 cm-1 indicates that short sequence


85

(TTTG) is dominant in the polar molecule chains.[29,118,119] Besides, the weak

intensity of the 614 cm-1 with the disappearance of the 760 cm-1 and the 976 cm-1 bands

indicates a minor amount of non-polar trans-gauche chains.[25] Hence, the PVDF@100

is predominantly a β/γ phase mixture. The formation of polar molecule chains in the low

temperature annealed samples can be attributed to the chemical interaction between

PVDF chains and either polar molecules of the DMF solvent or functional groups of

GO.[77,120] At current stage, it is difficult to identify which effect is dominant. For

PVDF@150, the absorption intensity of all bands increases compared with PVDF@100,

indicating an increased crystallinity with further evaporation of the residue solvents.

However, no new band emerges, and the crystal structure is identical to that of the

PVDF@100. With further increasing the temperature to 200°C, a significant increase in

the relative intensity of the 614 cm-1 band can be observed, followed by decreased all

trans peaks at 840 cm-1, 1230 cm-1 and 1271 cm-1, indicating the formation of non-polar

α phase.[25] For the nanocomposites 0.025-rGO@100 and 0.025-rGO@150, the ATR-

IR spectra show no difference with that of PVDF@100 and PVDF@150, as shown in

Figure 8.2(b). However, variations can be observed between PVDF@200 and 0.025-

rGO@200, where the decreased intensity of 1230 cm-1 is simultaneously associated by

the growing 840 cm-1 and 1271 cm-1 bands. This means, apart from transferring to non-

polar α phase, the γ phase is transferred to β phase.[36,119]


86

Figure 8.2 ATR-IR spectra comparing pure PVDF and rGO/PVDF nanocomposites at annealing temperatures ranging from 100°C to 200°C, with IR wavenumber between (a) 775cm-1 to 950cm-1, and (b) 975cm-1 to 1350cm-1

The melting temperature Tm of the pure PVDF is stated to be about 155°C~160°C in the

manufacture data sheets, and 160°C~180°C in the literatures depending on the

crystalline forms as well as processing method.[121-125] To ascertain the melting point

range of the PVDF polymer prepared in this research, we measured the dielectric

permittivity vs. temperature plots of both an as-casted 1.5-rGO and an as-casted pure

PVDF, which is plotted in Figure 8.3. Generally, the α-PVDF does not have a Curie

point, the temperature for the ferroelectric to paraelectric transition, and the β- and γ-

PVDF possess a curie temperature range overlapping with that of the melting

temperature.[126] This means the temperature where dielectric permittivity peaks can

be regarded as the melting point. As seen, the as-casted PVDF exhibits a peak dielectric

permittivity at about 156 °C~161 °C, which is in good agreement with that stated in the

manufacture data sheet. As for the as-casted 1.5-rGO, the dielectric permittivity ceased

to grow above ~ 122 °C, and a sharp decrease in dielectric permittivity was observed at

~169 °C. The wide temperature range for as-casted 1.5-rGO may not be solely assigned


87

to its melting behaviour but may also corelated to the reduction of GO. Still, it is

reasonable to claim a melting point lower than 169 °C due to the sharp decrease in

dielectric permittivity. Concerning the change in IR absorption with respect to

temperature, we therefore suggest that the molecular conformational transition occurs in

the melt-PVDF, and the TTTT molecular chains will pack to form the β phase on

cooling the melt. As it is quite natural that pure PVDF will recrystalize in the more

thermal-dynamically stable α phase, the contrasting results observed in the

nanocomposites highlights the effect of rGO in the formation TTTT molecular chains

and accordingly the β phase.

Figure 8.3 Dielectric permittivity vs. temperature plots for an as-casted 1.5-rGO and an as-casted pure PVDF


88

One limitation of the IR spectra is that it only shows the information of a single point on

the sample surface. The effective depth of penetration de of the IR beam for parallel and

perpendicular polarization can be calculated, respectively, as:[36,119]

2 2 2 21 2 1 2

2 2 2 2 2 2 2 2 21 2 1 2 2 1 2

cos 2 sin

( ) ( )sin sinparr

n n n nd

n n n n n n n

(8.2.1)

21 2

2 2 2 2 21 2 1 2

cos

( ) sinperp

n nd

n n n n

(8.2.2)

where n1, n2 is the reflective index of the ZnSe crystal and PVDF, θ is the incident angle

of the IR beam, and λ is the wavelength. The de is a mean value between dparr and dperp.

Therefore by taking n1=2.4 and n2=1.4 [127], the de associating to the IR beams

absorbed by 760 cm-1 and 840 cm-1 can be calculated as 5.74 µm and 5.06 µm. This

small incident area means the IR spectra may only represent the surface condition of the

sample films. Hence, addition information is still needed to study the microstructure of

the nanocomposites.

8.3 Crystalline Structure of the rGO/PVDF Nanocomposites

In this section, we will use the X-ray diffraction (XRD) to study the crystalline structure

of the rGO/PVDF nanocomposites. The XRD spectra of testing samples were measured

by an X-ray diffractor (Bruker D8 Advanced, Bruker, USA) with CuKα radiation

(1.5405 Å), with 2θ ranging from 10° to 140°.

Figure 8.4 shows the X-ray diffraction patterns for pure PVDF and the nanocomposites

reduced at 200°C for 1h. As seen, the X-ray radiation has a penetration higher than the

thickness of both PVDF and the nanocomposite films, as the sharp peak marked by the


89

* mark can be associated to the major diffractions of the Blu-Tack paste (Bostik, USA)

used to glue the samples on the testing stage. This means XRD spectra can provide a

complementary microstructure information for the nanocomposites.

Figure 8.4 XRD spectra for PVDF and nanocomposites annealed at 200°C, the peaks marked by * is assigned to the substrate

To show details of the crystalline structure, we have studied the XRD pattern in the

range between 2θ values of 14° to 25°, which are fitted with Lorenz function and shown

in Figure 8.5(a) to (e). The peaks at 17.7°, 18.4°, 19.6° in the pure PVDF pattern can be

assigned to (100), (020), and (110) planes, respectively, of the α phase while the

formation of a shoulder peak at 2θ=20.6°C in the nanocomposite pattern can be

assigned to either the (200) or the (110) planes of the β phase.[34,128] It can be

observed that a very broad peak exists at around 2θ = 19°, which can be associated to

the amorphous phase. We observed a growing intensity of β(200)/(110) as well as α(100)


90

diffractions with increasing rGO volume fraction, which indicate a direct relation

between rGO addition and β-PVDF transition.

Figure 8.5 Fitting curves with Lorenz peak function for (a) pure PVDF and (b) to (e) the nanocomposites reduced at 200°C

The major challenge in quantitatively analyse the XRD pattern for the PVDF and the

related composites is the overlapping of β(200) and β(110) diffractions due to the

analogous lattice spacing. In this research, we suggest the shoulder peak at around

2θ=20.6° may be assigned to β(110) diffraction. To start, we calculated the β phase

content X(β), which is plotted in Figure 8.3.3(a). Each point is an average of three

samples. The X(β) is defined as:

(200)/(110)

(200)/(110) (100) (020) (110)

( )I

XI I I I

(8.3.1)


91

where I is the intensity of X-ray diffractions. As seen, the increase in rGO content give

rise to a higher X(β), as the X(β) for 1.0-rGO@200 is merely 0.08, which was increased

to 0.32 for 2.5-rGO@200. This establishes a direct relation between rGO addition and

nucleation of the β-PVDF. As indicated in Figure 8.6, the addition of rGO also induced

a change in the intensity of the α(100) diffraction. However, the X(α(100)) does not

always increase with increasing rGO volume fraction, which is also indicated in Figure

8.6(a). This means the rGO may not have a direct impact on the nucleation of α-PVDF

with (100) orientation. By regarding the change in intensity of the α(100) diffraction as

a texture growth in α-PVDF, its texture quality F(α(100)), defined as:

100

(100)100 020 110

IF

I

(8.3.2)

is calculated and plotted in Figure 8.6(b). As seen, F(α(100)) increases with increasing

rGO volume fraction, indicating the addition of rGO can induce a preferred (100)

orientation in α-PVDF. One possible explanation of the rGO induced crystal structure

change in PVDF polymer is sketched in Figure 8.6(c). As X(β) is directly related to the

rGO content, it is reasonable to assume a layer of β-PVDF on the rGO surface. This

assumption is in accordance with the experimental and calculated results reported in the

literatures.[67,68,77,129] Comparing the result of X(β) and X(α(100)), it is claimed that

β phase possess the priority to form on the rGO surface and the α(100) may grow

epitaxially with β phase as substrates. This is supported in Figure 8.6(b) by the

increased FWHM of α(100) diffraction indicating increased density of defects due to

disordering at the α/β phase boundary. The parameter of α(100) lattice is 9.64Å*4.96Å

while that for the β(200) lattice is 4.91Å*2.56Å and for β(110) is 9.87Å*2.56Å.

Compared to the β(200), the β(110) lattice possesses a smaller lattice mismatching


92

hence is more likely to induce the epitaxial growth of the α crystals with (100)

orientation. Hence, we claim that the shoulder peak at 20.6° could mainly be assigned to

the β(110) diffraction, and the local structure on the rGO surface may be a layer of β

phase grafted with the α phase shell.

Figure 8.6 (a) content of β(110)/(200) and α(100) in the crystalline forms, (b) content of α(100) in the α phase and its FWHM changes with respect to the rGO volume fraction, and (c) illustration of the

β(110)/α(100) stack structure in the nanocomposite sample.


93

8.4 Morphology and Local Piezoelectric Response of the rGO/PVDF

Nanocomposites

In this section, we will study the morphology and local piezoelectric response of the

rGO/PVDF nanocomposites. An atomic force microscopy (AFM) (NTEGRA Prima,

NT-MDT Spectrum Instruments, Russia) with piezo-force microscopy (PFM) module

was used for the measurements. Details can be found in Chapter 5. The AC voltage

applied to the tip is 5V at 100Hz. The butterfly loops were measured by applied a -30V

to 30V DC voltage sweep to the samples.

Figure 8.7(a) and (b) show the morphology of a pure PVDF and a 1.0-rGO@200. As

seen, the nanocomposite exhibits a rougher surface compared to pure PVDF indicating

an agglomerated nucleation of PVDF polymer at the existence of rGO. We show each

agglomerate is packaged by α phase as evidenced by the covering spherulites composed

of folded TGT�̅ chains.[130] Meanwhile, we used piezo-force microscope (PFM) to

probe the electromechanical response for both samples. We applied a sweep voltage of -

30V to 30V onto selected points and captured the displacement loop, the results are

plotted in Figure 8.7(e), (f), and (g). As for nanocomposite, we found the

electromechanical response to be capacitive on top of the spherulites shell while

ferroelectric at the valley between individual agglomerates. This can be supported by

the hysteresis characteristics on the nanocomposite amplitude-voltage loop due to

saturation of the molecular dipole. As for the pure PVDF, its amplitude-voltage loop is

also linear, which is analogous to the spherulites shell of the nanocomposites. The PFM

results demonstrate that the β phase is locally heterogeneous in the nanocomposite. This

result supports the microstructure model in Figure 8.7(c). On top of the spherulites, a


94

thick α phase shell may predominantly contribute a capacitive response, while this shell

is thinned at the valley exposing more β phase to contribute a ferroelectric response.

Figure 8.7 AFM images for (a) 1.0-rGO@200 and (b) pure PVDF indicate the nanocomposite possess rougher surface of agglomerated spherulites, PFM images for (c) 1.0-rGO@200 and (d) pure PVDF show cross-talk signal from morphology fluctuation, therefore we applied a -30V to 30V DC sweep to individual points to test the local electromechanical response, which are plotted in (e) to (g)

8.5 Formation Mechanism of β Phase in the rGO/PVDF

Nanocomposites

In this section, we will discuss the formation mechanism of β phase in the rGO/PVDF

nanocomposites. Our experimental data in the above sections can establish a direct

relation between β phase formation and rGO content, which suggests a priory nucleation

of β phase in the nanocomposites. Besides, the β phase was only observed in the

nanocomposites reduced above the melting point, suggesting a melting-recrystallization


95

manner of the β phase formation mechanism. Concerning the removal of hydrophilic

groups in rGO upon heating the nanocomposites, it is unlikely to attribute the β phase

formation to the hydrogen bonds between rGO hydrophilic groups and TTTT chains.

One way to assess the formation mechanism of β phase formation from melt is from the

perspective of the system Gibbs free energy change. For a homogeneous nucleation, the

change of system Gibbs free energy ΔG is:

U SG G U E (8.5.1)

where ΔGU is the difference of Gibbs free energy per volume U between the solid and

melt, and ΔES is the different of surface energy between the solid and melt.[131,132]

Equation (8.5.1) well describes the nucleation of α phase in the pure PVDF. With the

addition of an extrinsic inclusion, the nucleation becomes heterogeneous due to the

catalyse effect of inclusion surface. The free Gibbs energy change for heterogenous

nucleation ΔG(θ) can be described as:

( ) ( )G Gf (8.5.2)

where 0≤θ≤π is the wetting angle.[133] When θ=π, equation (8.5.2) becomes equation

(8.5.1) and the nucleation is homogeneous. Comparing equation (8.5.1) and (8.5.2), it

can be indicated that the inclusions, such as rGO in this case, can accelerate the

nucleation. This, however, does not necessarily result in the nucleation of the

thermodynamically instable β phase. Modification of equation (8.5.2) concerning the

equalization between inclusion Fermi level and melt electrochemical potential has been

reported in many literatures, which added an energy saving ψ to volume free energy

change as:[134-136]


96

( ) (( ) ) ( )U SG G U E f (8.5.3)

Herein, we claim this equalization should exist in the contact of rGO and melt-PVDF

due to their differences in compositions. The Fermi level-electrochemical potential

equalization can result in rGO surface to be charged, either positively or negatively

depending on the relative position of its Fermi level, which will induce a screening

phenomenon in the melt-PVDF. According to this, there are good reasons to assume an

electrical double layer (EDL) structure in the melt-PVDF composed to screen the rGO

surface charge. This is illustrated in detail in Figure 8.5.1 (b). As illustrated, the

Helmholtz layer is constructed by a layer of tightly bonded TTTT molecules with its

built-in field counter-balances the electrostatic field of the rGO surface charge. After the

Helmholtz layer is the diffusion layer constructed by loosely absorbed TTTT molecules,

the rGO-PVDF interaction in this area is weaker than that in the Helmholtz layer as the

Stern potential is far smaller than the surface potential. The melt-PVDF in the EDL can

nucleate to the β phase on cooling the melt, which could be an explanation of the

growth of β phase on the rGO surface from the PVDF melt. According to the discussion

in Chapter 6, the rGO surface charge σ due to Fermi level equalization can be defined as:

0 (exp( ) 1)kT

(8.5.4)

where σ0 is the electron density of rGO. Regarding a fully flexible chain in the melt and

the polarization density p as the effective charge density of a TTTT chain, we can give

the criterion for TTTT chain absorption on the rGO surface as:

p (8.5.5)


97

This means the energy saving due to Fermi level equalization should be sufficiently

large to induce the TTTT transition, otherwise the PVDF will remain TGT �̅

conformation and nucleate to α phase. The β phase formation mechanism also indicate a

unique molecular dipole configuration on the rGO surface. As rGO is a planar particle

and is uniformly charged, the molecular dipole perpendicular to the rGO surface should

exhibit a dipole orientation mirrored by the rGO plane. This means the one rGO particle

with its nearby polar PVDF chains can construct a micron bimorph device, making the

nanocomposite self-polarized. This finding indicates the potential of using self-

polarized rGO/PVDF nanocomposites with symmetrical dipole configuration as an

actuator or sensor device. The direct piezoelectric response of the rGO/PVDF

nanocomposite is illustrated in detail in Figure 8.8 (c). When the nanocomposite

undergoes an upward/downward bending moment M, the PVDF dipoles on the

top/bottom of the rGO sheet will be stretched while those on the bottom/top will be

compressed. This dipole polarization/depolarization process will induce a potential

difference between the top and bottom surfaces of the rGO sheet, which is the

mechanism of piezoelectricity for the rGO/PVDF nanocomposite.


98

Figure 8.8 (a) Comparison of the homogeneous nucleation (N(homo)) in pure PVDF and heterogeneous nucleation (N(hetero)) in the nanocomposite, (b) β phase formation due to TTTT

molecule absorption and packaging at the rGO surface forming electrical double layer structure in the PVDF melt, assuming rGO is positively charged, the built-in field of the PVDF dipole (indicated

as an arrow) will counter-balance the static field of the rGO surface charge and (c) illustration of symmetrical PVDF dipole (white arrow) on the rGO surface (black line) surface forming a self-

bimorph in the nanocomposite

8.6 Summary

In this chapter, we studied the molecular and crystal structure of the rGO/PVDF

nanocomposites. The findings of this chapter can be listed as the followings:


99

(1) The ATR-IR spectra indicate the existence of TTTT PVDF chains confirm the

formation of β phase in the rGO/PVDF nanocomposites in the melting-

recrystallization procedure.

(2) X-ray diffraction shows a direct relation between β phase content and rGO

volume fraction. The volume fraction of up to 0.30 for β phase is obtained in

2.5-rGO@200. The formation of β phase also induces a(100)-orientation. This is

explained by an α/β stack model suggesting the β phase is packaged by an α

crystal shell.

(3) The AFM image clearly shows the spherulites structure dominate the

nanocomposite surface morphology, demonstrating the α phase shell. The PFM

image shows an inhomogeneous distribution of β phase at the valley of

spherulites for the nanocomposite sample. This inhomogeneity is explained as a

thinner α shell at the valley causes an exposure of the underneath β phase.

(4) A β phase formation mechanism is proposed based on the experimental data. We

suggest the equalization of rGO Fermi level and melt-PVDF electrochemical

potential charges the rGO surface constructing an electrical double layer (EDL)

in the melt. A tightly bonded layer of TTTT chains can therefore compose the

Helmholtz layer in the EDL forms the β phase on cooling the nanocomposites.

Besides, we also suggest the electrical dipole of the β phase exhibit a mirrored

orientation with respect to the rGO plane, this would result in a self-polarized

bimorph behaviour.


100

Chapter 9 rGO/PVDF Nanocomposite Related Devices

9.1 Introduction

In the last chapter, we showed the formation and self-alignment of the β phase in

rGO/PVDF nanocomposites, which made them piezoelectric without additional

treatment. Therefore, it will be interesting to know how these nanocomposites will

perform in smart devices. In this chapter, we report the fabrication and characterisation

of two prototype devices, an actuator and a flexible energy harvester, to study the

piezoelectric properties of the nanocomposites. This chapter is structured in the

following way.

The first part of this chapter is focused on the piezoelectric responses of the actuators.

We start from the device design and assembly procedure, followed by introducing the

set-up of the measuring system. The piezoelectric properties of the as-assembled device

were measured and compared with a commercial PVDF membrane. The unique self-

bimorph characteristics of the nanocomposites are discussed. The other part of this

chapter is about a flexible energy harvester, which is also assembled with the

nanocomposites. The configuration of the measurement as well as the device fabrication

is reported. The energy output characteristics was measured and discussed.

9.2 Actuator Assembly and Measurement Configuration

Piezoelectric materials can generate a strain response to an applied electric field, hence

can be assembled in an actuator for bending or vibration control applications. In this

section, the advantages and drawbacks of using rGO/PVDF nanocomposites in actuator

applications are evaluated.


101

Figure 9.1(a) shows the structure and mechanism of a bi-clamped actuator (BCA)

device with a polarized piezoelectric component. The ferroelectric domain is defined as

pointing downwards. The vibration of this BCA with an applied electric field E can be

attributed to the transverse piezoelectric effect defined as:

31 31S d E (9.2.1)

where S31 is the transverse strain and d31 is the transverse piezoelectric constant.[8,137]

If a positive electric field, defined as that in the same direction as the polarization, is

applied to the BCA, the device should generate a negative S31 to compensate for the

increase in S33. In the bi-clamped condition as shown in the figure, the S31 of the upper

surface is higher than that of the lower. This causes a negative curvature to the beam

due to surface tension. In terms of the device, a downward bending should be expected

and vice versa under a negative electric field. In this research, two BCAs were

fabricated, one with a commercial polarized PVDF film (Pizotech Arkema, France) with

thickness of 114 μm, and the other with a 1.5-rGO@200 nanocomposite with thickness

of 80μm. While the commercial PVDF film possess an Au electrode, the 1.5-rGO@200

was sputtered with Cr/Au electrode. Both samples were cut with a sharp knife to a 1 cm

× 0.5 cm rectangular tape. The BCA device is fabricated by gluing each end (~0.2 cm)

of the tapes on a glass substrate by a super glue (406, Loctite, France) and wiring the

front and back electrodes. The BCA device was then fixed on the testing stage. The

sputtering method was stated in detail in chapter 5. To measure this strain response of a

BCA device, we designed the testing method as shown in Figure 9.1(b). The

measurement equipments contain an oscilloscope (Picoscope 3206, Pico Technologies,

UK), a function generator (RS component, UK), a voltage amplifier (OEM MODEL


102

PA05039, Agilent Technologies, USA), a modular laser vibrometer (OFV2570, Polytec,

Germany), a positioning system consisting of two motorized translation stages for the x

and y axes (models 8TM173-20-50, 8TM173-20, STANDA, Italy). Briefly, the function

generator was connected to the voltage amplifier to deliver a parodic voltage signal to

the BCA. The monitor head of the laser vibrometer was hanged above the BCA and the

laser beam was focused on the centre of the BCA. The monitor head was connected to

its controller, and the collected displacement signal is delivered from the controller to

the oscilloscope. Both the applied voltage and displacement signals were monitored by

the Picoscope monitoring software program (Pico Technologies, UK).


103

Figure 9.1 (a) Vibration regime of a bi-clamped actuator device with respect to the electric field and (b) the vibration measurement configuration


104

9.3 Vibrational Characteristics of the Nanocomposite

Figure 9.2(a) and (b) compares the vibrational characteristics of BCAs fabricated with

the nanocomposites and a commercial polarized PVDF film. As seen, the PVDF-BCA

behaves as a single morph as illustrated in Figure 9.2(a), with a downward bending with

forward electric field and vice versa. The maximum centre displacement of the PVDF-

BCA measured at 100V/mm 20kHz was measured to be 3nm. While for the 1.5-

rGO@200-BCA, the centre displacements were found to be in-phase under forward and

reverse electric field. This is a bimorph behaviour demonstrating the intrinsic

symmetrical domain configuration at the rGO surface as discussed in Chapter 8. The

maximum centre displacement of the 1.5-rGO@200-BCA was measured to be 0.6 nm,

corresponding to 20% that of the commercial PVDF. Thus, we have demonstrated the

concept of a self-bimorph actuator utilizing the symmetrical dipole orientation on the

rGO surface. By testing the prototype devices, we have shown it is possible to use the

self-polarized piezoelectric composite as an alternative to the bulk counterparts where

electrical polarization may be difficult.


105

Figure 9.2 Strain responses of BCAs assembled with (a) commercial PVDF film and (b) 0.015-rGO@200 nanocomposite operating at 100V/mm 20kHz

It can be indicated from the strain response that the performance of 1.5-rGO@200-BCA

is inferior to that of the commercial PVDF-BCA in terms of the maximum device


106

displacement. This can be attributed to the limitations of the rGO/PVDF composites in

actuating applications. To begin with, the β phase content of 0.015-rGO@200 was

found to be only 0.12 and is embedded in the non-active α phase. The α phase shell

induces a substrate effect causing damping to the β phase vibration. The effort of

increasing β content was also found to be inefficient as an increase in the rGO volume

fraction introduces higher leakage to the nanocomposites and the device is very

vulnerable to the electric field. It was also found that device fabrication was only

successful for nanocomposites with 1.0 vol.% and 1.5 vol.% rGO, and only that with

1.5 vol.% could generate a measurable strain. Another drawback is the randomness in

rGO orientation. As the bending of the nanocomposite actuator device is amplified by

those of individual internal PVDF/rGO/PVDF bimorphs, the random rGO orientation

may reduce the effective strain in preferred directions. In addition, the XRD results

presented in Chapter 8 indicate a high content of amorphous phase in the

nanocomposites. The amorphous phase forms a soft polymer environment which not

only absorbs the vibration but also may introduce higher leakage to the nanocomposites.

Therefore, we suggest that significant optimisation of the rGO/PVDF nanocomposites

could be carried out resulting in high crystallinity and well-oriented rGO particles that

may generate an improved strain response in actuator applications.

9.4 Energy Harvester Assembly and Measurement Configuration

It is always demanding to scavenge energy from the environment to fight against the

energy crisis. This relies on the energy transfer from one form to another and storage

afterwards, which is possible by utilizing the unique nature of functional materials.

Piezoelectric material is one kind of these functional materials that could transfer the


107

vibrational energy into electrical energy, which can be used as a “battery-less” solution

for self-powered sensor networks.[138-141] In this section, we report the fabrication

and characterization of vibrational energy harvesters utilizing the piezoelectric response.

Figure 9.3(a) shows the structure of the energy harvester, which is composed of a

nanocomposite, wires, and insulating package. The nanocomposites with a thickness of

80μm were cut into a 1 cm × 1 cm square and were sputtered with Cr/Au electrode on

both surfaces. To wire the nanocomposites, two sections of cupper tape were cut and

connected on the nanocomposite by silver paste. The wires were then soldered to the

cupper tapes. After that, all elements were plastic-packaged to a device. Figure 9.3(b)

shows the graph of the vibration measurement configuration. One end of the energy

harvester was mechanically clamped by a metal cap that fixed on an electromagnetic

shaker (Gearing & Watson Electronics, UK) head and the other end is free to vibrate

with respect to the shaker vibration due to resonance. This will induce a bending stress

to the nanocomposites, which was monitored by a laser vibrometer (M5L/2, MEL,

Germany) and an accelerometer (4370, Brüel & Kjær, Denmark). Simultaneously, the

nanocomposite can react to the bending stress and generate a voltage difference between

electrodes. Both the bending signal and electrode signal was collected by an

oscilloscope (Pico 3206, Pico Technologies, UK) and monitored by the Picoscope

software on the computer. The input impedance of the oscilloscope is 1MΩ and the

maximum sampling rate of 1MS/s.


108

Figure 9.3 (a) Structure of a cantilever type energy harvester with rGO/PVDF nanocomposite and (b) the voltage output measurement configuration

Before measuring the energy harvester, it is important to verify that the output voltage

signal is contributed by the piezoelectric response rather than the cross talk of the


109

electromagnetic interference (EMI), and the contact potential change.[142-144] Figure

9.4 shows the voltage output of an energy harvester with 1.5-rGO@200. The harvester

is driven by finger tapping with the electromagnetic shaker being switched off. The

open circuit voltage at both (a) forward and (b) reverse connection with the oscilloscope

was measured. As polarity of the piezoelectric response is defined by that of the

ferroelectric domain, an opposite polarity can be observed when switching the

connection manner.[142] Thus, we define the upper side of the device after mounting on

the shaker head as positive and the other as negative. As can be seen in Figure 9.4, the

damping effect induces a free oscillation in the device, and a voltage output is captured

with respect to this oscillation. The damping ratio of the device can be defined as the

natural logarithm of the ratio of any two successive amplitudes in the free oscillations:

1ln( ) 2n

n

x

x (9.4.1)

where δ is the logarithmic decrement, x is the amplitude and ϛ is the damping ratio,

which was calculated to be 0.015 for the device under test.[145,146] An analogous

damping phenomenon was also found in the voltage output, which can be directly

associated to that of the free oscillation. This indicates that the voltage response is

piezoelectric. More importantly, the polarity of output voltage signal is switchable by

switching the polarity of the connection. As seen in Figure 9.4(a) and (b), under the

same strain cycle, a downwards voltage peak was captured under an upward bending

strain in the forward connection while the opposite manner is observed in the reverse

connection. The contrasting output characteristics between forward and reverse

connection can be associated to the polarity of the ferroelectric domain. Combining


110

these evidences, the voltage output of the device can be predominantly attribute to the

piezoelectric response of the nanocomposites.

Figure 9.4 Voltage output of a single-end-clamped energy harvester driven by finger tapping under (a) forward connection and (b) reverse connection


111

The energy harvester is an electromechanical coupled device in which the mechanical

energy should be efficiently delivered to the active piezoelectric component to

maximize the voltage output. As a single-end-clamped cantilever energy harvester, the

shape of the device can affect the output power.[143,147-149] It has been reported that

by using a trapezoidal shape, the device performance can be improved.[147-149] In this

research, we optimized the devices by reducing the cantilever free edge width. The

results are shown in Figure 9.5. As seen, by reducing the width ratio of free-edge to

clamped-edge from 1 to 0, the peak output voltage increases from 0.13V to 0.80V. This

could be attributed to the nanocomposite being bended more efficiently. Therefore, the

triangular cantilever was chosen as the optimized shape for devices fabricated in this

research.

Figure 9.5 Relation between cantilever shape and the voltage output for the energy harvester with 1.5-rGO@200


112

9.5 Output Characteristics of the Energy Harvesters

To further increase the bending stress of the triangular cantilever energy harvester

(TCEH), a hexagonal stainless-steel nut weighting 0.6 g with a diameter of 5 mm were

fixed at the free edge as a load mass. Figure 9.6(a) shows the peak voltage output vs.

load mass plots of the TCEH with 1.5-rGO@200 (simplified as 1.5-rGO-TCEH) driven

by the electromagnetic shaker at 10 Hz. The peak open circuit voltage VOC was 0.80 V

without load mass, which was increased to 1.79 V with a load mass of 1.2 g. However,

further increasing the load mass does not always increase the output voltage, as the VOC

dropped to 1.61 V at the load mass of 1.8g and further to 0.75 V at 2.4 g. Hence, the

1.2 g mass was applied to all other devices involved for further testing.

Figure 9.6 Open circuit voltage output vs. load mass for 1.5-rGO-TCEH

Table 9.5.1 shows output characteristics of the TCEHs assembled with nanocomposites

of different rGO volume fraction. These devices were fabricated with the method state


113

in section 9.4, with the dimension as shown in Figure 9.4.3. The devices were driven by

the electromagnetic shaker at 10Hz with a 1.2 g mass fixed at the free end of the device.

As seen, the VOC of 1.0-rGO-TCEH is 2.357 V, which is the maximum value among the

devices involved. This means that a higher rGO volume fraction does not lead to a

higher VOC to the device. As reported, the piezoelectric material is a capacitive voltage

source, and the voltage across the capacitor geometry can be affected by its leakage

behaviour.[139,144,150] It has been shown in the previous chapters that the reduced

tunnelling distance with increasing rGO volume fraction introduces a higher leakage in

high rGO content nanocomposites. This could be the reason for the decreased voltage

output in high rGO content devices. The power output of these TCEHs have been

measured with the existence of a resistive load. Three load resistors RL with resistance

of 10 kΩ, 100 kΩ, and 1MΩ were connected to the device, and the voltage across the RL

were captured. The output power P to the resistive load is calculated from:

2

L

VP

R (9.5.1)

For instance, the VL across a 1MΩ resistor is 1.434 V for 1.0-rGO-TCEH and results is

a power density of 0.182 mW/cm3. The power output can be modified by the choice of

RL. According to the impedance matching theory, the output power maximizes when the

RL matches with the impedance of the device. For devices with rGO volume fraction

between 1.0 vol.% and 2.0 vol.%, the maximum output power is observed when

connected to a 1MΩ while that with 2.5 vol.% rGO is observed for a 100 kΩ load. This

demonstrates the impact of load resistance on the power output. Meanwhile, we also

measured the output energy density over a period of a voltage cycle. The energy density

J per peak voltage circle can be defined as:


114

2

1

( )t

tJ P t dt

where t1 and t2 are the start and end time of an individual voltage cycle respectively and

P(t) is the instantaneous power density. As seen in Table 9.5.1, the maximum energy

density was found to be 0.055 μJ/cm3 for 1.0-rGO-TCEH when connected to a 1MΩ

load. The energy output behaviour also indicates the internal screening effect. This

appears as a decreased time span Δt per voltage cycle with increasing rGO volume

fraction. The Δt was found to be 0.60ms, 0.40ms, 0.20ms, and 0.16ms for

nanocomposite devices with 1.0 vol.%, 1.5 vol.%, 2.0 vol.% and 2.5 vol.% rGO,

respectively. Both the power output and energy output show the impact of internal

screening phenomena hindering the device performance. This effect is illustrated in

Figure 9.5.2. The defects and impurities can be regarded as free charge carriers which

are mobile in an electric field. A stress applied on the piezoelectric material can induce

a dipole moment, and accordingly a built-in electric field is generated. This built-in

electric field promotes the internal motion of free carriers, which neutralized the trapped

charge. Hence, the effect of the strain induced dipole moment is screened, and the

macroscopic behaviour observed is a short time span as well as a low peak voltage

response. In terms of the device with high rGO volume fraction, the carrier travelling

distance is sufficiently reduced. This may increase the screening rate and thus causes

weaker output behaviour. These results reveal a paradox in the composite related energy

harvester device. The output performance is strongly dependent on the quality of

heterostructure of the inclusion/matrix interface, which highlights inclusions with

superb conductance.[142] But a highly conductive inclusion in turn causes significant


115

internal screening and results in high leakage. The effect needs to be addressed in the

future works for composite related energy harvester devices.

Table 9.5.1 Output Characteristics of TCEHs assembled with pure PVDF and rGO/PVDF nanocomposites

Device VOC (V) Load Resistance

(Ω)

Peak Output

Voltage (V)

Power Density

(mW/cm3)

Energy

Density

(μJ/cm3)

1.0-rGO-TCEH

10k 0.035 0.011 0.003

2.357 100k 0.403 0.141 0.042

1M 1.434 0.182 0.055

1.5-rGO-TCEH

10k 0.025 0.005 0.001

1.79 100k 0.246 0.054 0.011

1M 1.154 0.117 0.024

2.0-rGO-TCEH

10k 0.018 0.003 0.0003

0.262 100k 0.081 0.006 0.0006

1M 0.393 0.014 0.0014

2.5-rGO-TCEH

10k 0.004 0.002 -

0.178 100k 0.034 0.012 0.002

1M 0.064 0.004 -


116

Figure 9.7 Illustration of the internal screening effect in a capacitive device.

9.6 Summary

In this chapter, we have evaluated the piezoelectric performance of the rGO/PVDF

nanocomposites by incorporating them into both actuator and energy harvester devices.

The findings in this chapter can be summarized as the follows:

(1) We have designed and tested a bi-clamped actuator with a 1.5-rGO@200, which

exhibits a bimorph behaviour in contrast to the unimorph behaviour of that with

a commercial PVDF film. This supports that the molecular dipole is symmetrical

to the rGO plane forming micron bimorph structure. The major limitation of

actuator devices based on self-polarized composites is that they are more

vulnerable to the electric field compared to bulk materials. This limits the efforts

of improving the actuating performance by increasing the rGO volume fraction.


117

(2) We have designed and tested a series of cantilever type energy harvesters with

rGO/PVDF nanocomposites. We show the strategy of using a triangular device

shape to enhance the output performance of the energy harvester device. A 1.0-

rGO device can deliver a power density of 0.182 mW/cm3 and energy density of

0.055 μJ/cm3 to a 1MΩ load, which is the best among the devices fabricated.

The nanocomposite devices are hindered by the internal screening effect induced

by reduced carrier tunnelling distance at higher rGO volume fractions. This

results in a decrease in both power and energy output in devices with high rGO

volume fractions.


118

Chapter 10 Conclusion and future work

10.1 Conclusion

This project is a systematic study on the dielectric and piezoelectric properties of the

rGO/PVDF nanocomposites, particularly, the effect of rGO/PVDF heterostructure on

the device performances. These nanocomposites were fabricated via an in-situ thermal

reduction method, with graphite-oxide (GO) particles as the starting inclusion material

to avoid agglomeration. The GO particles were thermally reduced in-situ in the PVDF

polymer to recover their electrical conductivity.

To start, an ideal conductor/insulator model was used to study the dielectric behaviour

of the rGO/PVDF nanocomposites. This studied is based on the understanding that the

inclusion particles can effectively expand the system electrode area of a composite.

With the Schottky diode theory, we found the improved dielectric response in a

composite over its matrix could be attributed to the formation of inclusion/matrix

heterostructures providing more charge blocking sites. This explains why nano-sized,

conductive inclusion particles can lead to a significant enhancement in the composite

dielectric response. Besides, we also found a carrier recombination induced pseudo-

leakage on charging a composite, which results in an exponentially decay in the

capacitor energy efficiency. The possibility of carrier recombination increases in the

same sense as the dielectric response, indicating that composites with large dielectric

permittivity is more likely to exhibit a high leakage.

The model proposed in this research has been supported by the dielectric properties

observed in the rGO/PVDF nanocomposites. To start, the addition of rGO improved the


119

dielectric permittivity of the PVDF polymer. The maximum dielectric permittivity

observed in this research is 380 (1 kHz) for 2.5-rGO@200, compared to that of 11

(1 kHz) for the pure PVDF. Simultaneously, the rGO particles were also well dispersed

in the PVDF polymer. This is supported by the small value and weak dependence of the

nanocomposite tanδ on the rGO content. As expected, nanocomposite with such a large

dielectric permittivity failed to generate a large discharge energy density due to high

leakage. The maximum discharge energy density for nanocomposite samples was

merely 0.09 J/cm3 (1.0-rGO@200, 30 MV/m, 10Hz), which is limited by their weak

dielectric strength as well as small energy efficiency. By studying the charging

characteristics of the samples, we demonstrated the predominant contribution of charge

carrier recombination phenomena to the system leakage. We also showed the most

efficient way to improve the nanocomposite discharge energy density is to increase the

effective series resistance of the rGO/PVDF heterostructures. This was accomplished by

utilizing the temperature tuneable nature of rGO. The energy efficiency for the 1.5-

rGO@160 is 0.65 (50MV/m, 10Hz), resulting in a discharge energy density of 0.67

J/cm3 that is 3 times that of the pure PVDF at the same condition. Furthermore, we

established an explicit relation between dielectric permittivity and energy efficiency for

PVDF composites. This relation can be used to evaluate the discharge energy density

for PVDF composites, which fits well with the experimental data.

The structural change in the PVDF polymer induced by the addition of rGO particles

was also studied. Comparison of the molecular and crystalline structure between pure

PVDF and the rGO/PVDF nanocomposites was carried out by measuring their IR

spectra and XRD patterns. Contrary to the predominant non-polar α phase structure

observed in 200 °C annealed PVDF samples, up to 0.32 of the β phase was observed in


120

the 200 °C reduced nanocomposites. We showed the as-cast PVDF and nanocomposites

exhibit the same γ phase dominated structure, which may be attributed to the effect of

polar DMF solvents. Variations start to emerge in samples annealed above melting

temperature. This demonstrates that the β phase in the nanocomposites forms from a

melting-recrystallization procedure, which is also accompanied by the removal of

hydrophilic groups on rGO. Combining observation from the XRD and AFM/PFM, we

show evidences of the β phase crystals grow on the surface of rGO and are covered by

the α phase. The formation of the β phase is explained by an electrochemical interaction

model. The rGO surface is charged due to Fermi level equalization with PVDF melt,

which absorbs TTTT chains to construct the electrical double layer to screen the surface

charge.

The β phase formation mechanism indicate that the rGO/PVDF nanocomposite reduced

at 200°C is (i) piezoelectric and (ii) self-polarized, and electrochemical interaction

between TTTT chains and the rGO particle may also suggest a mirrored molecular

dipole by the rGO plane. Two types of piezoelectric devices, namely an actuator and a

generator were fabricated with the 200°C reduced nanocomposites. The actuator device

is designed in the way of a bi-clamped cantilever to evaluate the unique mirrored

molecular dipole configuration. Compared to that assembled with a commercial PVDF

film, the actuator with 1.5-rGO@200 exhibited a bimorph behaviour when switching

the polarity of the wire connection. This supports the mirrored molecular dipole as

suggested by the β phase formation mechanism. As for the generator, the maximum

open circuit voltage was 2.357V for a device assembled with 1.0-rGO@200, with the

maximum output power density and energy density of 0.182 mW/cm3, and 0.055 μJ/cm3,

respectively, delivered to a 1MΩ load. Simultaneously, we showed that the addition of


121

rGO accelerates the internal screening in the nanocomposite device. This is evidenced

by the shorter time span per output cycle observed with increasing rGO volume fraction.

The internal screening causes reduced power and energy output for devices with higher

rGO volume fractions, which needs to be addressed for further optimizing the device

energy harvesting performances.

10.2 Future work

Flexible, lightweight ferroelectric materials have a broad prospective in the next-

generation electronic devices such as bendable screens, self-powered sensor networks,

wearable equipment, and inflatable aerospace structures. In this research, we

demonstrate that rGO/PVDF composites have the potential to be used in high power

capacitor, sensor, and actuator applications.

In terms of the capacitors, we would suggest using nano-sized, semi-conductive

inclusion particles as alternatives to the partially reduced rGO to increase the

temperature stability of the composite dielectric behaviour. Meanwhile, it would also be

a good option to use a high permittivity matrix material such as poly(vinylidene

fluoride-co-hexafluoropropylene), and poly(vinylidene fluoride-trifluoroethylene-

chlorofluoroethylene) to further improve the energy storage performance. In the device

perspective, the nanocomposite films can be laminated to fabricate a multi-layer

capacitor (MLCC) device. They can be a lightweight and more accessible alternative to

the ferroelectric ceramics as the co-sintering is not needed in fabricating a

nanocomposite MLCC.

In terms of the piezoelectric energy harvesters and actuators, the device structure

optimization to increase the electro-mechanical coupling may overwhelm the effect of


122

property-increase in the active materials. However, we still suggest an improved

orientation of rGO particles to the electric field direction may improve the device

piezoelectric response. This calls for more advanced processing routes to fabricate the

rGO/PVDF nanocomposites.


123

Reference

[1] V. E. Henrich and P. A. Cox, The surface science of metal oxides (Cambridge university press, 1996).

[2] A. Mandelis and C. Christofides, Physics, chemistry and technology of solid state gas sensor devices (John Wiley & Sons, 1993), Vol. 174.

[3] L. H. Dawson, Physical Review 29, 532 (1927).

[4] J. Curie and P. Curie, Journal de Physique Théorique et Appliquée 1, 245 (1882).

[5] G. Lippmann, Journal de Physique Théorique et Appliquée 10, 381 (1881).

[6] B. Jaffe, Piezoelectric ceramics (Elsevier, 2012), Vol. 3.

[7] Z. L. Wang, Journal of Physics: Condensed Matter 16, R829 (2004).

[8] ANSI/IEEE Std 176-1987, 0_1 (1988).

[9] A. Erturk and D. J. Inman, in Piezoelectric Energy Harvesting (John Wiley & Sons, Ltd, 2011), pp. 343.

[10] S. E. Lyshevski, Nano-and micro-electromechanical systems: fundamentals of nano-and microengineering (CRC press, 2005), Vol. 8.

[11] M. R. Kermani, M. Moallem, and R. V. Patel, Applied vibration suppression using piezoelectric materials (Nova Publishers, 2008).

[12] A. A. Marino, Modern bioelectricity (CRC Press, 1988).

[13] M. E. Lines and A. M. Glass, Principles and applications of ferroelectrics and related materials (Oxford university press, 1977).

[14] M. Vijaya, Piezoelectric materials and devices: Applications in engineering and medical sciences (CRC Press, 2012).

[15] B. Wul and I. Goldman, Compt. rend. Acad. sci. URSS 46, 139 (1945).

[16] G. Kwei, A. Lawson, S. Billinge, and S. Cheong, The Journal of Physical Chemistry 97, 2368 (1993).

[17] R. V. Latham, British Journal of Applied Physics 18, 1383 (1967).

[18] M. Stewart, M. Cain, and D. Hall, Ferroelectric hysteresis measurement and analysis (National Physical Laboratory Teddington, 1999).

[19] H. YAN, F. INAM, G. VIOLA, H. NING, H. ZHANG, Q. JIANG, T. ZENG, Z. GAO, and M. J. REECE, Journal of Advanced Dielectrics 01, 107 (2011).

[20] J. F. Scott, Journal of Physics: Condensed Matter 20, 021001 (2008).


124

[21] T. Wentink, L. J. Willwerth, and J. P. Phaneuf, Journal of Polymer Science 55, 551 (1961).

[22] A. Liquori, in Journal of Polymer Science: Polymer Symposia (Wiley Online Library, 1966), pp. 209.

[23] G. Cortili and G. Zerbi, Spectrochimica Acta Part A: Molecular Spectroscopy 23, 285 (1967).

[24] G. Cortili and G. Zerbi, Spectrochimica Acta Part A: Molecular Spectroscopy 23, 2216 (1967).

[25] M. Li, H. J. Wondergem, M. J. Spijkman, K. Asadi, I. Katsouras, P. W. Blom, and D. M. de Leeuw, Nature materials 12, 433 (2013).

[26] J. B. Lando, H. G. Olf, and A. Peterlin, Journal of Polymer Science Part A-1: Polymer Chemistry 4, 941 (1966).

[27] R. Hasegawa, Y. Takahashi, Y. Chatani, and H. Tadokoro, Polym J 3, 600 (1972).

[28] V. Ranjan, L. Yu, M. B. Nardelli, and J. Bernholc, Physical review letters 99, 047801 (2007).

[29] M. A. Bachmann, W. L. Gordon, J. L. Koenig, and J. B. Lando, Journal of Applied Physics 50, 6106 (1979).

[30] S. Weinhold, M. H. Litt, and J. B. Lando, Macromolecules 13, 1178 (1980).

[31] Y. Takahashi and H. Tadokoro, Macromolecules 13, 1317 (1980).

[32] K. Tashiro, M. Kobayashi, and H. Tadokoro, Macromolecules 14, 1757 (1981).

[33] T. Furukawa, Phase Transitions 18, 143 (1989).

[34] C.-h. Du, B.-K. Zhu, and Y.-Y. Xu, Journal of Applied Polymer Science 104, 2254 (2007).

[35] Y. Wang, M. Cakmak, and J. L. White, Journal of applied polymer science 30, 2615 (1985).

[36] G. T. Davis, J. E. McKinney, M. G. Broadhurst, and S. C. Roth, Journal of Applied Physics 49, 4998 (1978).

[37] R. G. Kepler and R. A. Anderson, Journal of Applied Physics 49, 1232 (1978).

[38] Y. Takahashi, Y. Nakagawa, H. Miyaji, and K. Asai, Journal of Polymer Science Part C: Polymer Letters 25, 153 (1987).

[39] Y. Song, Y. Shen, H. Liu, Y. Lin, M. Li, and C.-W. Nan, Journal of Materials Chemistry 22, 16491 (2012).


125

[40] L. Gao, J. He, J. Hu, and Y. Li, The Journal of Physical Chemistry C 118, 831 (2014).

[41] D. Chun-gang, W. N. Mei, J. R. Hardy, S. Ducharme, C. Jaewu, and P. A. Dowben, EPL (Europhysics Letters) 61, 81 (2003).

[42] Prateek, V. K. Thakur, and R. K. Gupta, Chemical reviews 116, 4260 (2016).

[43] S. Maji, P. K. Sarkar, L. Aggarwal, S. K. Ghosh, D. Mandal, G. Sheet, and S. Acharya, Physical chemistry chemical physics : PCCP 17, 8159 (2015).

[44] D. Shah, P. Maiti, E. Gunn, D. F. Schmidt, D. D. Jiang, C. A. Batt, and E. P. Giannelis, Advanced Materials 16, 1173 (2004).

[45] A. Javadi, Y. Xiao, W. Xu, and S. Gong, Journal of Materials Chemistry 22, 830 (2012).

[46] M. Li, C. Gao, H. Hu, and Z. Zhao, Carbon 65, 371 (2013).

[47] Y. Mao, S. Mao, Z.-G. Ye, Z. Xie, and L. Zheng, Journal of Applied Physics 108, 014102 (2010).

[48] K. Yang, X. Huang, Y. Huang, L. Xie, and P. Jiang, Chemistry of Materials 25, 2327 (2013).

[49] H. Luo, D. Zhang, C. Jiang, X. Yuan, C. Chen, and K. Zhou, ACS Applied Materials & Interfaces 7, 8061 (2015).

[50] N. Levi, R. Czerw, S. Xing, P. Iyer, and D. L. Carroll, Nano letters 4, 1267 (2004).

[51] F. He, S. Lau, H. L. Chan, and J. Fan, Advanced Materials 21, 710 (2009).

[52] R. K. Layek, S. Samanta, D. P. Chatterjee, and A. K. Nandi, Polymer 51, 5846 (2010).

[53] D. Wang, Y. Bao, J. W. Zha, J. Zhao, Z. M. Dang, and G. H. Hu, ACS Appl Mater Interfaces 4, 6273 (2012).

[54] K. Yang, X. Huang, L. Fang, J. He, and P. Jiang, Nanoscale 6, 14740 (2014).

[55] J. I. Paredes, S. Villar-Rodil, A. Martínez-Alonso, and J. M. D. Tascón, Langmuir 24, 10560 (2008).

[56] L. Cui, X. Lu, D. Chao, H. Liu, Y. Li, and C. Wang, physica status solidi (a) 208, 459 (2011).

[57] H. Tang, G. J. Ehlert, Y. Lin, and H. A. Sodano, Nano letters 12, 84 (2012).

[58] P. Arunachalam, in Polymer-based Nanocomposites for Energy and Environmental Applications, edited by M. M. Khan (Woodhead Publishing, 2018), pp. 185.


126

[59] K. Lichtenecker, Physikalische Zeitschrift 27, 115 (1926).

[60] M. Garnet, Philos. Trans. R. Soc. London, Ser. A 205, 237 (1906).

[61] T. C. Choy, Effective medium theory: principles and applications (Oxford University Press, 2015), Vol. 165.

[62] V. D. Bruggeman, Annalen der physik 416, 636 (1935).

[63] T. J. Lewis, Dielectrics and Electrical Insulation, IEEE Transactions on 1, 812 (1994).

[64] R. Armstrong and B. Horrocks, Solid State Ionics 94, 181 (1997).

[65] T. Tanaka, M. Kozako, N. Fuse, and Y. Ohki, IEEE transactions on dielectrics and electrical insulation 12, 669 (2005).

[66] J. I. Roscow, C. R. Bowen, and D. P. Almond, ACS Energy Letters 2, 2264 (2017).

[67] P. Martins, C. M. Costa, M. Benelmekki, G. Botelho, and S. Lanceros-Mendez, CrystEngComm 14, 2807 (2012).

[68] D. Mandal, K. J. Kim, and J. S. Lee, Langmuir : the ACS journal of surfaces and colloids 28, 10310 (2012).

[69] M. M. Alam, A. Sultana, D. Sarkar, and D. Mandal, Nanotechnology 28, 365401 (2017).

[70] R. Tian, Q. Xu, C. Lu, X. Duan, and R. G. Xiong, Chemical communications 53, 7933 (2017).

[71] S. Yu, W. Zheng, W. Yu, Y. Zhang, Q. Jiang, and Z. Zhao, Macromolecules 42, 8870 (2009).

[72] J. Wang, H. Li, J. Liu, Y. Duan, S. Jiang, and S. Yan, Journal of the American Chemical Society 125, 1496 (2003).

[73] D. C. Bassett and A. Keller, Philosophical Magazine 6, 345 (1961).

[74] D. C. Bassett, Philosophical Magazine 6, 1053 (1961).

[75] N. Taniguchi and A. Kawaguchi, Macromolecules 38, 4761 (2005).

[76] S. Manna and A. K. Nandi, The Journal of Physical Chemistry C 111, 14670 (2007).

[77] K. Ke, P. Pötschke, D. Jehnichen, D. Fischer, and B. Voit, Polymer 55, 611 (2014).

[78] M. J. Baker, C. S. Hughes, and K. A. Hollywood, in Biophotonics: Vibrational Spectroscopic Diagnostics (Morgan & Claypool Publishers, 2016), pp. 2.

[79] R. Proksch, Journal of Applied Physics 118, 072011 (2015).


127

[80] A. Labuda and R. Proksch, Applied Physics Letters 106, 253103 (2015).

[81] A. Di Bartolomeo, Physics Reports 606, 1 (2016).

[82] E. Fermi, Rendiconti Lincei 145 (1926).

[83] P. A. M. Dirac, Proc. R. Soc. Lond. A 112, 661 (1926).

[84] C. Kittel, Introduction to solid state physics (Wiley, 2005).

[85] R. T. Tung, Materials Science and Engineering: R: Reports 35, 1 (2001).

[86] S. M. Sze and K. K. Ng, Physics of semiconductor devices (John wiley & sons, 2006).

[87] S. Grover and G. Moddel, IEEE Journal of Photovoltaics 1, 78 (2011).

[88] M. Nagae, Japanese Journal of Applied Physics 11, 1611 (1972).

[89] K. Szot, W. Speier, G. Bihlmayer, and R. Waser, Nature materials 5, 312 (2006).

[90] J. Y. Li, C. Huang, and Q. Zhang, Applied Physics Letters 84, 3124 (2004).

[91] J. Y. Li, L. Zhang, and S. Ducharme, Applied Physics Letters 90, 132901 (2007).

[92] Z. M. Dang, J. K. Yuan, S. H. Yao, and R. J. Liao, Adv Mater 25, 6334 (2013).

[93] H. Liu, Y. Shen, Y. Song, C. W. Nan, Y. Lin, and X. Yang, Adv Mater 23, 5104 (2011).

[94] Z. M. Dang, L. Wang, Y. Yin, Q. Zhang, and Q. Q. Lei, Advanced Materials 19, 852 (2007).

[95] H.-K. Jeong et al., Journal of the American Chemical Society 130, 1362 (2008).

[96] H.-K. Jeong, Y. P. Lee, M. H. Jin, E. S. Kim, J. J. Bae, and Y. H. Lee, Chemical Physics Letters 470, 255 (2009).

[97] M. Acik, G. Lee, C. Mattevi, M. Chhowalla, K. Cho, and Y. J. Chabal, Nature materials 9, 840 (2010).

[98] M. Acik, C. Mattevi, C. Gong, G. Lee, K. Cho, M. Chhowalla, and Y. J. Chabal, ACS Nano 4, 5861 (2010).

[99] A. Bagri, C. Mattevi, M. Acik, Y. J. Chabal, M. Chhowalla, and V. B. Shenoy, Nature chemistry 2, 581 (2010).

[100] C.-E. Cheng, C.-Y. Lin, C.-H. Shan, S.-Y. Tsai, K.-W. Lin, C.-S. Chang, and F. Shih-Sen Chien, Journal of Applied Physics 114, 014503 (2013).

[101] C. Brabec, U. Scherf, and V. Dyakonov, Organic photovoltaics: materials, device physics, and manufacturing technologies (John Wiley & Sons, 2011).


128

[102] J.-H. Im, J. Chung, S.-J. Kim, and N.-G. Park, Nanoscale research letters 7, 353 (2012).

[103] N. Jalali, PhD thesis, Queen Mary University of London, UK (2015)

[104] S. Kochowski and K. Nitsch, Thin Solid Films 415, 133 (2002).

[105] S. H. Huh, Thermal reduction of graphene oxide (INTECH Open Access Publisher, 2011).

[106] O. C. Compton, B. Jain, D. A. Dikin, A. Abouimrane, K. Amine, and S. T. Nguyen, ACS Nano 5, 4380 (2011).

[107] H. F. Liang, C. T. G. Smith, C. A. Mills, and S. R. P. Silva, J. Mater. Chem. C 3, 12484 (2015).

[108] A. Mathkar, D. Tozier, P. Cox, P. Ong, C. Galande, K. Balakrishnan, A. Leela Mohana Reddy, and P. M. Ajayan, The journal of physical chemistry letters 3, 986 (2012).

[109] L. Sygellou, G. Paterakis, C. Galiotis, and D. Tasis, The Journal of Physical Chemistry C 120, 281 (2016).

[110] I. Jung, D. A. Dikin, R. D. Piner, and R. S. Ruoff, Nano letters 8, 4283 (2008).

[111] Q. Zhang, H. Li, M. Poh, F. Xia, Z.-Y. Cheng, H. Xu, and C. Huang, Nature 419, 284 (2002).

[112] L. Wang and Z.-M. Dang, Applied Physics Letters 87, 042903 (2005).

[113] Q. Chen, P. Du, L. Jin, W. Weng, and G. Han, Applied Physics Letters 91, 022912 (2007).

[114] C.-W. Nan, Progress in Materials Science 37, 1 (1993).

[115] V. Ranjan, M. B. Nardelli, and J. Bernholc, Physical review letters 108, 087802 (2012).

[116] D. Mandal, K. Henkel, and D. Schmeisser, The Journal of Physical Chemistry B 115, 10567 (2011).

[117] J. C. Li, C. L. Wang, W. L. Zhong, P. L. Zhang, Q. H. Wang, and J. F. Webb, Applied Physics Letters 81, 2223 (2002).

[118] S. Weinhold, M. Litt, and J. Lando, Macromolecules 13, 1178 (1980).

[119] M. Kobayashi, K. Tashiro, and H. Tadokoro, Macromolecules 8, 158 (1975).

[120] K. Tashiro, H. Tadokoro, and M. Kobayashi, Ferroelectrics 32, 167 (1981).

[121] L. Ruan, X. Yao, Y. Chang, L. Zhou, G. Qin, and X. Zhang, Polymers 10, 228 (2018).


129

[122] P. Martins, A. C. Lopes, and S. Lanceros-Mendez, Progress in Polymer Science 39, 683 (2014).

[123] J. Gregorio, Rinaldo and M. Cestari, Journal of Polymer Science Part B: Polymer Physics 32, 859 (1994).

[124] R. Gregorio, Journal of Applied Polymer Science 100, 3272 (2006).

[125] R. Imamura, A. Silva, and R. Gregorio Jr, Journal of applied polymer science 110, 3242 (2008).

[126] A. J. Lovinger, D. D. Davis, R. E. Cais, and J. M. Kometani, Macromolecules 19, 1491 (1986).

[127] M. Li, I. Katsouras, C. Piliego, G. Glasser, I. Lieberwirth, P. W. M. Blom, and D. M. de Leeuw, Journal of Materials Chemistry C 1, 7695 (2013).

[128] Y. Takahashi, Y. Nakagawa, H. Miyaji, and K. Asai, Journal of Polymer Science Part C: Polymer Letters 25, 153 (1987).

[129] C. L. Liang, Z. H. Mai, Q. Xie, R. Y. Bao, W. Yang, B. H. Xie, and M. B. Yang, The journal of physical chemistry. B 118, 9104 (2014).

[130] A. Keller, Philosophical Magazine 2, 1171 (1957).

[131] D. Turnbull, The Journal of Chemical Physics 20, 411 (1952).

[132] K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich, and D. Turnbull (Academic Press, 1991), pp. 75.

[133] D. Turnbull, The Journal of Chemical Physics 18, 198 (1950).

[134] R. F. Tournier, Physica B: Condensed Matter 392, 79 (2007).

[135] R. Tournier, (Iron Steel Institute Japan, 2006).

[136] R. F. Tournier, Science and technology of advanced materials 10, 014607 (2009).

[137] T. Jordan, N. Ounaies, ICASE Report No. 2001-28.

[138] K. I. Park et al., Adv Mater 24, 2999 (2012).

[139] J. Briscoe, M. Stewart, M. Vopson, M. Cain, P. M. Weaver, and S. Dunn, Advanced Energy Materials 2, 1261 (2012).

[140] C. K. Jeong, K.-I. Park, J. Ryu, G.-T. Hwang, and K. J. Lee, Advanced Functional Materials 24, 2620 (2014).

[141] S. Lee et al., Advanced Functional Materials 23, 2445 (2013).

[142] R. Yang, Y. Qin, C. Li, L. Dai, and Z. L. Wang, Applied Physics Letters 94, 022905 (2009).


130

[143] C. R. Bowen, H. A. Kim, P. M. Weaver, and S. Dunn, Energy & Environmental Science 7, 25 (2014).

[144] N. Jalali, P. Woolliams, M. Stewart, P. M. Weaver, M. G. Cain, S. Dunn, and J. Briscoe, Journal of Materials Chemistry A 2, 10945 (2014).

[145] X. Chen, S. Xu, N. Yao, and Y. Shi, Nano letters 10, 2133 (2010).

[146] J. Park, M. Kim, Y. Lee, H. S. Lee, and H. Ko, Science advances 1, e1500661 (2015).

[147] M. I. Friswell and S. Adhikari, Journal of Applied Physics 108, 014901 (2010).

[148] J. M. Dietl and E. Garcia, Journal of Intelligent Material Systems and Structures 21, 633 (2010).

[149] D. Benasciutti, L. Moro, S. Zelenika, and E. Brusa, Microsystem Technologies 16, 657 (2009).

[150] J. Liu, P. Fei, J. Song, X. Wang, C. Lao, R. Tummala, and Z. L. Wang, Nano letters 8, 328 (2008).


131

Publications

Y Zhang, Y Wang, TW Button, Local Polarization Transits Polar Molecular Chain in

rGO/PVDF Nanocomposite for High Power Density Nanogenerator, to be submitted

Y Zhang, TW Button, Origin of Leakage for High Dielectric Permittivity Composite

Capacitors, to be submitted

Y Zhang, Y Wang, S Qi, S Dunn, H Dong, TW Button, Enhanced Discharge Energy

Density in the rGO/PVDF Nanocomposites: the Role of Heterointerface, Applied

Physics Letters 112, 202904, 2018

Y Jiang, Z Qiu, R McPhillips, C Meggs, S Mahboob, H Wang, R Duncan, D Rodriguez-

Sanmartin, Y Zhang, G Schiavone, R Eisma, M Desmulliez, S Eljamel, S Cochran, TW

Button, C Demore, IEEE Transactions of Ultrasonics, Ferroelectrics and Frequency

Control 63 (2), 2016

L Luo, C Chen, H Luo, Y Zhang, K Zhou, D Zhang, The Effects of Precursors on the

Morphology and Microstructure of Potassium Sodium Niobate Nanorods Synthesized

by Molten Salt Synthesis, CrystEngComm 17, 8710-8719, 2015

Y Zhang, Y Jiang, X Lin, R Xie, K Zhou, TW Button, D Zhang, Fine‐Scaled

Piezoelectric Ceramic/Polymer 2‐2 Composites for High‐Frequency Transducer,

Journal of the American Ceramic Society 97 (4), 1060-1064, 2014

dielectric and piezoelectric properties of reduced-graphite...

Documents